6(x+3)(x-1)-6(x-1)=-5(x+3)

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Solution for 6(x+3)(x-1)-6(x-1)=-5(x+3) equation: 


Simplifying
6(x + 3)(x + -1) + -6(x + -1) = -5(x + 3)

Reorder the terms:
6(3 + x)(x + -1) + -6(x + -1) = -5(x + 3)

Reorder the terms:
6(3 + x)(-1 + x) + -6(x + -1) = -5(x + 3)

Multiply (3 + x) * (-1 + x)
6(3(-1 + x) + x(-1 + x)) + -6(x + -1) = -5(x + 3)
6((-1 * 3 + x * 3) + x(-1 + x)) + -6(x + -1) = -5(x + 3)
6((-3 + 3x) + x(-1 + x)) + -6(x + -1) = -5(x + 3)
6(-3 + 3x + (-1 * x + x * x)) + -6(x + -1) = -5(x + 3)
6(-3 + 3x + (-1x + x2)) + -6(x + -1) = -5(x + 3)

Combine like terms: 3x + -1x = 2x
6(-3 + 2x + x2) + -6(x + -1) = -5(x + 3)
(-3 * 6 + 2x * 6 + x2 * 6) + -6(x + -1) = -5(x + 3)
(-18 + 12x + 6x2) + -6(x + -1) = -5(x + 3)

Reorder the terms:
-18 + 12x + 6x2 + -6(-1 + x) = -5(x + 3)
-18 + 12x + 6x2 + (-1 * -6 + x * -6) = -5(x + 3)
-18 + 12x + 6x2 + (6 + -6x) = -5(x + 3)

Reorder the terms:
-18 + 6 + 12x + -6x + 6x2 = -5(x + 3)

Combine like terms: -18 + 6 = -12
-12 + 12x + -6x + 6x2 = -5(x + 3)

Combine like terms: 12x + -6x = 6x
-12 + 6x + 6x2 = -5(x + 3)

Reorder the terms:
-12 + 6x + 6x2 = -5(3 + x)
-12 + 6x + 6x2 = (3 * -5 + x * -5)
-12 + 6x + 6x2 = (-15 + -5x)

Solving
-12 + 6x + 6x2 = -15 + -5x

Solving for variable 'x'.

Reorder the terms:
-12 + 15 + 6x + 5x + 6x2 = -15 + -5x + 15 + 5x

Combine like terms: -12 + 15 = 3
3 + 6x + 5x + 6x2 = -15 + -5x + 15 + 5x

Combine like terms: 6x + 5x = 11x
3 + 11x + 6x2 = -15 + -5x + 15 + 5x

Reorder the terms:
3 + 11x + 6x2 = -15 + 15 + -5x + 5x

Combine like terms: -15 + 15 = 0
3 + 11x + 6x2 = 0 + -5x + 5x
3 + 11x + 6x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
3 + 11x + 6x2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {-1.5, -0.3333333333}

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