6x(x+2)=(2x+4)(x+2)

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Solution for 6x(x+2)=(2x+4)(x+2) equation: 


Simplifying
6x(x + 2) = (2x + 4)(x + 2)

Reorder the terms:
6x(2 + x) = (2x + 4)(x + 2)
(2 * 6x + x * 6x) = (2x + 4)(x + 2)
(12x + 6x2) = (2x + 4)(x + 2)

Reorder the terms:
12x + 6x2 = (4 + 2x)(x + 2)

Reorder the terms:
12x + 6x2 = (4 + 2x)(2 + x)

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

Combine like terms: 4x + 4x = 8x
12x + 6x2 = (8 + 8x + 2x2)

Solving
12x + 6x2 = 8 + 8x + 2x2

Solving for variable 'x'.

Reorder the terms:
-8 + 12x + -8x + 6x2 + -2x2 = 8 + 8x + 2x2 + -8 + -8x + -2x2

Combine like terms: 12x + -8x = 4x
-8 + 4x + 6x2 + -2x2 = 8 + 8x + 2x2 + -8 + -8x + -2x2

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

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

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

Combine like terms: 8x + -8x = 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 + x + x2) = 0

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

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-2, 1}

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