Solve for X in 5(x+3)=0: Step-by-Step Solution

Q: Why can't I just divide everything by 5 first?

You absolutely can divide by 5 first! Since $ \frac{5(x+3)}{5} = \frac{0}{5} $, you get $ x+3 = 0 $ directly. Both methods work perfectly.

Q: What if the number outside wasn't 5 but was 0?

If you had $ 0(x+3) = 0 $, then any value of x would work! Zero times anything equals zero, so all real numbers would be solutions.

Q: Do I need to expand 5(x+3) to solve this?

Not necessarily! You can solve it two ways: Method 1: Divide by 5 first: (x+3) = 0Method 2: Expand to 5x + 15 = 0, then solveBoth give the same answer: x = -3

Q: How do I know which method is faster?

When you have a coefficient times parentheses equal to zero, dividing by the coefficient first is usually quicker. Save expanding for when you need to combine like terms or have more complex expressions.

Q: What does it mean that the product equals zero?

The Zero Product Property says: if A × B = 0, then either A = 0 or B = 0 (or both). Here, since 5 ≠ 0, we know (x+3) must equal 0.

Linear Equations with Zero Products

Solve x:

$5(x+3)=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine X

00:03 Open parentheses multiplying by each factor

00:15 Arrange the equation so that only one side has the unknown X

00:21 Isolate X

00:30 Here is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve x:

$5(x+3)=0$

Step-by-step solution

We open the parentheses according to the formula:

$a(x+b)=ax+ab$

$5\times x+5\times3=0$

$5x+15=0$

We will move the 15 to the right section and keep the corresponding sign:

$5x=-15$

Divide both sections by 5

$\frac{5x}{5}=\frac{-15}{5}$

$x=-3$

Final Answer

$-3$

Key Points to Remember

Essential concepts to master this topic

Zero Product Rule: If a product equals zero, one factor must be zero
Technique: Since 5 ≠ 0, then (x+3) must equal 0
Check: Substitute x = -3: 5(-3+3) = 5(0) = 0 ✓

Common Mistakes

Avoid these frequent errors

Dividing by the coefficient first
Don't divide both sides by 5 to get (x+3) = 0 immediately! Students often think this skips a step, but it's actually the correct approach. Always recognize that when a product equals zero, at least one factor must be zero.

Practice Quiz

Test your knowledge with interactive questions

$$ 5x=0 $$

FAQ

Everything you need to know about this question

Why can't I just divide everything by 5 first?

You absolutely can divide by 5 first! Since $\frac{5(x+3)}{5} = \frac{0}{5}$ , you get $x+3 = 0$ directly. Both methods work perfectly.

What if the number outside wasn't 5 but was 0?

If you had $0(x+3) = 0$ , then any value of x would work! Zero times anything equals zero, so all real numbers would be solutions.

Do I need to expand 5(x+3) to solve this?

Not necessarily! You can solve it two ways:

Method 1: Divide by 5 first: (x+3) = 0
Method 2: Expand to 5x + 15 = 0, then solve

Both give the same answer: x = -3

How do I know which method is faster?

When you have a coefficient times parentheses equal to zero, dividing by the coefficient first is usually quicker. Save expanding for when you need to combine like terms or have more complex expressions.

What does it mean that the product equals zero?

The Zero Product Property says: if A × B = 0, then either A = 0 or B = 0 (or both). Here, since 5 ≠ 0, we know (x+3) must equal 0.

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