6x(x+1)=(2x+8)(x+1)

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Solution for 6x(x+1)=(2x+8)(x+1) equation: 


Simplifying
6x(x + 1) = (2x + 8)(x + 1)

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

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

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

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

Combine like terms: 8x + 2x = 10x
6x + 6x2 = (8 + 10x + 2x2)

Solving
6x + 6x2 = 8 + 10x + 2x2

Solving for variable 'x'.

Reorder the terms:
-8 + 6x + -10x + 6x2 + -2x2 = 8 + 10x + 2x2 + -8 + -10x + -2x2

Combine like terms: 6x + -10x = -4x
-8 + -4x + 6x2 + -2x2 = 8 + 10x + 2x2 + -8 + -10x + -2x2

Combine like terms: 6x2 + -2x2 = 4x2
-8 + -4x + 4x2 = 8 + 10x + 2x2 + -8 + -10x + -2x2

Reorder the terms:
-8 + -4x + 4x2 = 8 + -8 + 10x + -10x + 2x2 + -2x2

Combine like terms: 8 + -8 = 0
-8 + -4x + 4x2 = 0 + 10x + -10x + 2x2 + -2x2
-8 + -4x + 4x2 = 10x + -10x + 2x2 + -2x2

Combine like terms: 10x + -10x = 0
-8 + -4x + 4x2 = 0 + 2x2 + -2x2
-8 + -4x + 4x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-8 + -4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + -1x + x2) = 0

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

Ignore the factor 4.

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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1

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 = {-1, 2}

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