(x+4)*(x+2)-(x+2)*x=(x+2)*x

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Solution for (x+4)*(x+2)-(x+2)*x=(x+2)*x equation: 


Simplifying
(x + 4)(x + 2) + -1(x + 2) * x = (x + 2) * x

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

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

Multiply (4 + x) * (2 + x)
(4(2 + x) + x(2 + x)) + -1(x + 2) * x = (x + 2) * x
((2 * 4 + x * 4) + x(2 + x)) + -1(x + 2) * x = (x + 2) * x
((8 + 4x) + x(2 + x)) + -1(x + 2) * x = (x + 2) * x
(8 + 4x + (2 * x + x * x)) + -1(x + 2) * x = (x + 2) * x
(8 + 4x + (2x + x2)) + -1(x + 2) * x = (x + 2) * x

Combine like terms: 4x + 2x = 6x
(8 + 6x + x2) + -1(x + 2) * x = (x + 2) * x

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

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

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

Combine like terms: 6x + -2x = 4x
8 + 4x + x2 + -1x2 = (x + 2) * x

Combine like terms: x2 + -1x2 = 0
8 + 4x + 0 = (x + 2) * x
8 + 4x = (x + 2) * x

Reorder the terms:
8 + 4x = (2 + x) * x

Reorder the terms for easier multiplication:
8 + 4x = x(2 + x)
8 + 4x = (2 * x + x * x)
8 + 4x = (2x + x2)

Solving
8 + 4x = 2x + x2

Solving for variable 'x'.

Combine like terms: 4x + -2x = 2x
8 + 2x + -1x2 = 2x + x2 + -2x + -1x2

Reorder the terms:
8 + 2x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
8 + 2x + -1x2 = 0 + x2 + -1x2
8 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + 2x + -1x2 = 0

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


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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 = {4, -2}

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