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

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Solution for 6(x+1)-2(x-1)(x+1)=-3(x-1) equation: 


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

Reorder the terms:
6(1 + x) + -2(x + -1)(x + 1) = -3(x + -1)
(1 * 6 + x * 6) + -2(x + -1)(x + 1) = -3(x + -1)
(6 + 6x) + -2(x + -1)(x + 1) = -3(x + -1)

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

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

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

Combine like terms: -1x + 1x = 0
6 + 6x + -2(-1 + 0 + x2) = -3(x + -1)
6 + 6x + -2(-1 + x2) = -3(x + -1)
6 + 6x + (-1 * -2 + x2 * -2) = -3(x + -1)
6 + 6x + (2 + -2x2) = -3(x + -1)

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

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

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

Solving
8 + 6x + -2x2 = 3 + -3x

Solving for variable 'x'.

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

Combine like terms: 8 + -3 = 5
5 + 6x + 3x + -2x2 = 3 + -3x + -3 + 3x

Combine like terms: 6x + 3x = 9x
5 + 9x + -2x2 = 3 + -3x + -3 + 3x

Reorder the terms:
5 + 9x + -2x2 = 3 + -3 + -3x + 3x

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

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

Factor a trinomial.
(5 + -1x)(1 + 2x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {5, -0.5}

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