(x+4)(2x-3)-(2x-3)=0

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Solution for (x+4)(2x-3)-(2x-3)=0 equation: 


Simplifying
(x + 4)(2x + -3) + -1(2x + -3) = 0

Reorder the terms:
(4 + x)(2x + -3) + -1(2x + -3) = 0

Reorder the terms:
(4 + x)(-3 + 2x) + -1(2x + -3) = 0

Multiply (4 + x) * (-3 + 2x)
(4(-3 + 2x) + x(-3 + 2x)) + -1(2x + -3) = 0
((-3 * 4 + 2x * 4) + x(-3 + 2x)) + -1(2x + -3) = 0
((-12 + 8x) + x(-3 + 2x)) + -1(2x + -3) = 0
(-12 + 8x + (-3 * x + 2x * x)) + -1(2x + -3) = 0
(-12 + 8x + (-3x + 2x2)) + -1(2x + -3) = 0

Combine like terms: 8x + -3x = 5x
(-12 + 5x + 2x2) + -1(2x + -3) = 0

Reorder the terms:
-12 + 5x + 2x2 + -1(-3 + 2x) = 0
-12 + 5x + 2x2 + (-3 * -1 + 2x * -1) = 0
-12 + 5x + 2x2 + (3 + -2x) = 0

Reorder the terms:
-12 + 3 + 5x + -2x + 2x2 = 0

Combine like terms: -12 + 3 = -9
-9 + 5x + -2x + 2x2 = 0

Combine like terms: 5x + -2x = 3x
-9 + 3x + 2x2 = 0

Solving
-9 + 3x + 2x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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 = {-3, 1.5}

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