(2x+3)(2x+3)-6x-9=0

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Solution for (2x+3)(2x+3)-6x-9=0 equation: 


Simplifying
(2x + 3)(2x + 3) + -6x + -9 = 0

Reorder the terms:
(3 + 2x)(2x + 3) + -6x + -9 = 0

Reorder the terms:
(3 + 2x)(3 + 2x) + -6x + -9 = 0

Multiply (3 + 2x) * (3 + 2x)
(3(3 + 2x) + 2x * (3 + 2x)) + -6x + -9 = 0
((3 * 3 + 2x * 3) + 2x * (3 + 2x)) + -6x + -9 = 0
((9 + 6x) + 2x * (3 + 2x)) + -6x + -9 = 0
(9 + 6x + (3 * 2x + 2x * 2x)) + -6x + -9 = 0
(9 + 6x + (6x + 4x2)) + -6x + -9 = 0

Combine like terms: 6x + 6x = 12x
(9 + 12x + 4x2) + -6x + -9 = 0

Reorder the terms:
9 + -9 + 12x + -6x + 4x2 = 0

Combine like terms: 9 + -9 = 0
0 + 12x + -6x + 4x2 = 0
12x + -6x + 4x2 = 0

Combine like terms: 12x + -6x = 6x
6x + 4x2 = 0

Solving
6x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(3 + 2x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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 = {0, -1.5}

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