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

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


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

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

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

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

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

Add '9' to each side of the equation.
-9 + 9 + 4x2 = -9 + 9 + 9x

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

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

Solving
4x2 = 9x

Solving for variable 'x'.

Reorder the terms:
-9x + 4x2 = 9x + -9x

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-9 + 4x) = 0


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 '(-9 + 4x)' equal to zero and attempt to solve:

Simplifying
-9 + 4x = 0

Solving
-9 + 4x = 0

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

Add '9' to each side of the equation.
-9 + 9 + 4x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 4x = 0 + 9
4x = 0 + 9

Combine like terms: 0 + 9 = 9
4x = 9

Divide each side by '4'.
x = 2.25

Simplifying
x = 2.25
Solution
x = {0, 2.25}

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