(x-3)(x+4)-(3x-2)2=x-8x(x-1)

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Solution for (x-3)(x+4)-(3x-2)2=x-8x(x-1) equation: 


Simplifying
(x + -3)(x + 4) + -1(3x + -2) * 2 = x + -8x(x + -1)

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

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

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

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

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

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

Multiply -1 * 2
-12 + 1x + x2 + -2(-2 + 3x) = x + -8x(x + -1)
-12 + 1x + x2 + (-2 * -2 + 3x * -2) = x + -8x(x + -1)
-12 + 1x + x2 + (4 + -6x) = x + -8x(x + -1)

Reorder the terms:
-12 + 4 + 1x + -6x + x2 = x + -8x(x + -1)

Combine like terms: -12 + 4 = -8
-8 + 1x + -6x + x2 = x + -8x(x + -1)

Combine like terms: 1x + -6x = -5x
-8 + -5x + x2 = x + -8x(x + -1)

Reorder the terms:
-8 + -5x + x2 = x + -8x(-1 + x)
-8 + -5x + x2 = x + (-1 * -8x + x * -8x)
-8 + -5x + x2 = x + (8x + -8x2)

Combine like terms: x + 8x = 9x
-8 + -5x + x2 = 9x + -8x2

Solving
-8 + -5x + x2 = 9x + -8x2

Solving for variable 'x'.

Reorder the terms:
-8 + -5x + -9x + x2 + 8x2 = 9x + -8x2 + -9x + 8x2

Combine like terms: -5x + -9x = -14x
-8 + -14x + x2 + 8x2 = 9x + -8x2 + -9x + 8x2

Combine like terms: x2 + 8x2 = 9x2
-8 + -14x + 9x2 = 9x + -8x2 + -9x + 8x2

Reorder the terms:
-8 + -14x + 9x2 = 9x + -9x + -8x2 + 8x2

Combine like terms: 9x + -9x = 0
-8 + -14x + 9x2 = 0 + -8x2 + 8x2
-8 + -14x + 9x2 = -8x2 + 8x2

Combine like terms: -8x2 + 8x2 = 0
-8 + -14x + 9x2 = 0

Factor a trinomial.
(-4 + -9x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -9x)' equal to zero and attempt to solve:

Simplifying
-4 + -9x = 0

Solving
-4 + -9x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -9x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -9x = 0 + 4
-9x = 0 + 4

Combine like terms: 0 + 4 = 4
-9x = 4

Divide each side by '-9'.
x = -0.4444444444

Simplifying
x = -0.4444444444

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.4444444444, 2}

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