(x+2)(x+4)=(3x+2)(x+2)

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Solution for (x+2)(x+4)=(3x+2)(x+2) equation: 


Simplifying
(x + 2)(x + 4) = (3x + 2)(x + 2)

Reorder the terms:
(2 + x)(x + 4) = (3x + 2)(x + 2)

Reorder the terms:
(2 + x)(4 + x) = (3x + 2)(x + 2)

Multiply (2 + x) * (4 + x)
(2(4 + x) + x(4 + x)) = (3x + 2)(x + 2)
((4 * 2 + x * 2) + x(4 + x)) = (3x + 2)(x + 2)
((8 + 2x) + x(4 + x)) = (3x + 2)(x + 2)
(8 + 2x + (4 * x + x * x)) = (3x + 2)(x + 2)
(8 + 2x + (4x + x2)) = (3x + 2)(x + 2)

Combine like terms: 2x + 4x = 6x
(8 + 6x + x2) = (3x + 2)(x + 2)

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

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

Multiply (2 + 3x) * (2 + x)
8 + 6x + x2 = (2(2 + x) + 3x * (2 + x))
8 + 6x + x2 = ((2 * 2 + x * 2) + 3x * (2 + x))
8 + 6x + x2 = ((4 + 2x) + 3x * (2 + x))
8 + 6x + x2 = (4 + 2x + (2 * 3x + x * 3x))
8 + 6x + x2 = (4 + 2x + (6x + 3x2))

Combine like terms: 2x + 6x = 8x
8 + 6x + x2 = (4 + 8x + 3x2)

Solving
8 + 6x + x2 = 4 + 8x + 3x2

Solving for variable 'x'.

Reorder the terms:
8 + -4 + 6x + -8x + x2 + -3x2 = 4 + 8x + 3x2 + -4 + -8x + -3x2

Combine like terms: 8 + -4 = 4
4 + 6x + -8x + x2 + -3x2 = 4 + 8x + 3x2 + -4 + -8x + -3x2

Combine like terms: 6x + -8x = -2x
4 + -2x + x2 + -3x2 = 4 + 8x + 3x2 + -4 + -8x + -3x2

Combine like terms: x2 + -3x2 = -2x2
4 + -2x + -2x2 = 4 + 8x + 3x2 + -4 + -8x + -3x2

Reorder the terms:
4 + -2x + -2x2 = 4 + -4 + 8x + -8x + 3x2 + -3x2

Combine like terms: 4 + -4 = 0
4 + -2x + -2x2 = 0 + 8x + -8x + 3x2 + -3x2
4 + -2x + -2x2 = 8x + -8x + 3x2 + -3x2

Combine like terms: 8x + -8x = 0
4 + -2x + -2x2 = 0 + 3x2 + -3x2
4 + -2x + -2x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
4 + -2x + -2x2 = 0

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

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

Ignore the factor 2.

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 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {1, -2}

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