(2x+3)(4x+5)-(4x^2-9)=0

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Solution for (2x+3)(4x+5)-(4x^2-9)=0 equation: 


Simplifying
(2x + 3)(4x + 5) + -1(4x2 + -9) = 0

Reorder the terms:
(3 + 2x)(4x + 5) + -1(4x2 + -9) = 0

Reorder the terms:
(3 + 2x)(5 + 4x) + -1(4x2 + -9) = 0

Multiply (3 + 2x) * (5 + 4x)
(3(5 + 4x) + 2x * (5 + 4x)) + -1(4x2 + -9) = 0
((5 * 3 + 4x * 3) + 2x * (5 + 4x)) + -1(4x2 + -9) = 0
((15 + 12x) + 2x * (5 + 4x)) + -1(4x2 + -9) = 0
(15 + 12x + (5 * 2x + 4x * 2x)) + -1(4x2 + -9) = 0
(15 + 12x + (10x + 8x2)) + -1(4x2 + -9) = 0

Combine like terms: 12x + 10x = 22x
(15 + 22x + 8x2) + -1(4x2 + -9) = 0

Reorder the terms:
15 + 22x + 8x2 + -1(-9 + 4x2) = 0
15 + 22x + 8x2 + (-9 * -1 + 4x2 * -1) = 0
15 + 22x + 8x2 + (9 + -4x2) = 0

Reorder the terms:
15 + 9 + 22x + 8x2 + -4x2 = 0

Combine like terms: 15 + 9 = 24
24 + 22x + 8x2 + -4x2 = 0

Combine like terms: 8x2 + -4x2 = 4x2
24 + 22x + 4x2 = 0

Solving
24 + 22x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 11x + 2x2) = 0

Factor a trinomial.
2((4 + x)(3 + 2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {-4, -1.5}

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