(2x-3)(2x+1)=3x-6

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Solution for (2x-3)(2x+1)=3x-6 equation: 


Simplifying
(2x + -3)(2x + 1) = 3x + -6

Reorder the terms:
(-3 + 2x)(2x + 1) = 3x + -6

Reorder the terms:
(-3 + 2x)(1 + 2x) = 3x + -6

Multiply (-3 + 2x) * (1 + 2x)
(-3(1 + 2x) + 2x * (1 + 2x)) = 3x + -6
((1 * -3 + 2x * -3) + 2x * (1 + 2x)) = 3x + -6
((-3 + -6x) + 2x * (1 + 2x)) = 3x + -6
(-3 + -6x + (1 * 2x + 2x * 2x)) = 3x + -6
(-3 + -6x + (2x + 4x2)) = 3x + -6

Combine like terms: -6x + 2x = -4x
(-3 + -4x + 4x2) = 3x + -6

Reorder the terms:
-3 + -4x + 4x2 = -6 + 3x

Solving
-3 + -4x + 4x2 = -6 + 3x

Solving for variable 'x'.

Reorder the terms:
-3 + 6 + -4x + -3x + 4x2 = -6 + 3x + 6 + -3x

Combine like terms: -3 + 6 = 3
3 + -4x + -3x + 4x2 = -6 + 3x + 6 + -3x

Combine like terms: -4x + -3x = -7x
3 + -7x + 4x2 = -6 + 3x + 6 + -3x

Reorder the terms:
3 + -7x + 4x2 = -6 + 6 + 3x + -3x

Combine like terms: -6 + 6 = 0
3 + -7x + 4x2 = 0 + 3x + -3x
3 + -7x + 4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
3 + -7x + 4x2 = 0

Factor a trinomial.
(3 + -4x)(1 + -1x) = 0


Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0.75, 1}

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