Resolve the Equation: 5x² + 7x + 9 = (2x-1)(2x+1)

Solve the following equation:

^{$5x^{2}+7x+9=(2x-1)(2x+1)$}

Let's begin by focusing on the right side of the equation:

$(2x-1)(2x+1)$

We must first open the parentheses whilst multiplying all the terms as needed:

$2x\cdot2x+2x\cdot1+-1\cdot2x+-1\cdot1$

$4x^2+2x-2x-1$
$4x^2-1$

Let's now return to the original equation, and move all terms to the same side.

$5X^2+7x+9=4X^2-1$
$5X^2-4X^2+7x+9+1=0$
$X^2+7X+10=0$

We are left with a simple quadratic equation, which can be solved using any method we desire (factoring or the quadratic formula).

Therefore the final solution is:

$X= -2,-5$