(2x-3)(x+1)=4(2x-3)

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Solution for (2x-3)(x+1)=4(2x-3) equation: 


Simplifying
(2x + -3)(x + 1) = 4(2x + -3)

Reorder the terms:
(-3 + 2x)(x + 1) = 4(2x + -3)

Reorder the terms:
(-3 + 2x)(1 + x) = 4(2x + -3)

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

Combine like terms: -3x + 2x = -1x
(-3 + -1x + 2x2) = 4(2x + -3)

Reorder the terms:
-3 + -1x + 2x2 = 4(-3 + 2x)
-3 + -1x + 2x2 = (-3 * 4 + 2x * 4)
-3 + -1x + 2x2 = (-12 + 8x)

Solving
-3 + -1x + 2x2 = -12 + 8x

Solving for variable 'x'.

Reorder the terms:
-3 + 12 + -1x + -8x + 2x2 = -12 + 8x + 12 + -8x

Combine like terms: -3 + 12 = 9
9 + -1x + -8x + 2x2 = -12 + 8x + 12 + -8x

Combine like terms: -1x + -8x = -9x
9 + -9x + 2x2 = -12 + 8x + 12 + -8x

Reorder the terms:
9 + -9x + 2x2 = -12 + 12 + 8x + -8x

Combine like terms: -12 + 12 = 0
9 + -9x + 2x2 = 0 + 8x + -8x
9 + -9x + 2x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
9 + -9x + 2x2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1.5, 3}

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