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

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


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

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

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

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

Combine like terms: -3x + 1x = -2x
3(-3 + -2x + x2) = (2x + -1)(x + -1) + 8
(-3 * 3 + -2x * 3 + x2 * 3) = (2x + -1)(x + -1) + 8
(-9 + -6x + 3x2) = (2x + -1)(x + -1) + 8

Reorder the terms:
-9 + -6x + 3x2 = (-1 + 2x)(x + -1) + 8

Reorder the terms:
-9 + -6x + 3x2 = (-1 + 2x)(-1 + x) + 8

Multiply (-1 + 2x) * (-1 + x)
-9 + -6x + 3x2 = (-1(-1 + x) + 2x * (-1 + x)) + 8
-9 + -6x + 3x2 = ((-1 * -1 + x * -1) + 2x * (-1 + x)) + 8
-9 + -6x + 3x2 = ((1 + -1x) + 2x * (-1 + x)) + 8
-9 + -6x + 3x2 = (1 + -1x + (-1 * 2x + x * 2x)) + 8
-9 + -6x + 3x2 = (1 + -1x + (-2x + 2x2)) + 8

Combine like terms: -1x + -2x = -3x
-9 + -6x + 3x2 = (1 + -3x + 2x2) + 8

Reorder the terms:
-9 + -6x + 3x2 = 1 + 8 + -3x + 2x2

Combine like terms: 1 + 8 = 9
-9 + -6x + 3x2 = 9 + -3x + 2x2

Solving
-9 + -6x + 3x2 = 9 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
-9 + -9 + -6x + 3x + 3x2 + -2x2 = 9 + -3x + 2x2 + -9 + 3x + -2x2

Combine like terms: -9 + -9 = -18
-18 + -6x + 3x + 3x2 + -2x2 = 9 + -3x + 2x2 + -9 + 3x + -2x2

Combine like terms: -6x + 3x = -3x
-18 + -3x + 3x2 + -2x2 = 9 + -3x + 2x2 + -9 + 3x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-18 + -3x + 1x2 = 9 + -3x + 2x2 + -9 + 3x + -2x2

Reorder the terms:
-18 + -3x + 1x2 = 9 + -9 + -3x + 3x + 2x2 + -2x2

Combine like terms: 9 + -9 = 0
-18 + -3x + 1x2 = 0 + -3x + 3x + 2x2 + -2x2
-18 + -3x + 1x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
-18 + -3x + 1x2 = 0 + 2x2 + -2x2
-18 + -3x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-18 + -3x + 1x2 = 0

Factor a trinomial.
(-3 + -1x)(6 + -1x) = 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 '(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
Solution
x = {-3, 6}

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