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

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


Simplifying
x2 + -1x = (x + -4)(2x + 3)

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

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

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

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

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

Solving
-1x + x2 = -12 + -5x + 2x2

Solving for variable 'x'.

Reorder the terms:
12 + -1x + 5x + x2 + -2x2 = -12 + -5x + 2x2 + 12 + 5x + -2x2

Combine like terms: -1x + 5x = 4x
12 + 4x + x2 + -2x2 = -12 + -5x + 2x2 + 12 + 5x + -2x2

Combine like terms: x2 + -2x2 = -1x2
12 + 4x + -1x2 = -12 + -5x + 2x2 + 12 + 5x + -2x2

Reorder the terms:
12 + 4x + -1x2 = -12 + 12 + -5x + 5x + 2x2 + -2x2

Combine like terms: -12 + 12 = 0
12 + 4x + -1x2 = 0 + -5x + 5x + 2x2 + -2x2
12 + 4x + -1x2 = -5x + 5x + 2x2 + -2x2

Combine like terms: -5x + 5x = 0
12 + 4x + -1x2 = 0 + 2x2 + -2x2
12 + 4x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
12 + 4x + -1x2 = 0

Factor a trinomial.
(6 + -1x)(2 + x) = 0


Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2
Solution
x = {6, -2}

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