(2x-3)(4x+3)=2x-3

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Solution for (2x-3)(4x+3)=2x-3 equation: 


Simplifying
(2x + -3)(4x + 3) = 2x + -3

Reorder the terms:
(-3 + 2x)(4x + 3) = 2x + -3

Reorder the terms:
(-3 + 2x)(3 + 4x) = 2x + -3

Multiply (-3 + 2x) * (3 + 4x)
(-3(3 + 4x) + 2x * (3 + 4x)) = 2x + -3
((3 * -3 + 4x * -3) + 2x * (3 + 4x)) = 2x + -3
((-9 + -12x) + 2x * (3 + 4x)) = 2x + -3
(-9 + -12x + (3 * 2x + 4x * 2x)) = 2x + -3
(-9 + -12x + (6x + 8x2)) = 2x + -3

Combine like terms: -12x + 6x = -6x
(-9 + -6x + 8x2) = 2x + -3

Reorder the terms:
-9 + -6x + 8x2 = -3 + 2x

Solving
-9 + -6x + 8x2 = -3 + 2x

Solving for variable 'x'.

Reorder the terms:
-9 + 3 + -6x + -2x + 8x2 = -3 + 2x + 3 + -2x

Combine like terms: -9 + 3 = -6
-6 + -6x + -2x + 8x2 = -3 + 2x + 3 + -2x

Combine like terms: -6x + -2x = -8x
-6 + -8x + 8x2 = -3 + 2x + 3 + -2x

Reorder the terms:
-6 + -8x + 8x2 = -3 + 3 + 2x + -2x

Combine like terms: -3 + 3 = 0
-6 + -8x + 8x2 = 0 + 2x + -2x
-6 + -8x + 8x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-6 + -8x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -4x + 4x2) = 0

Factor a trinomial.
2((-1 + -2x)(3 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

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 = {-0.5, 1.5}

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