(x+4)(x+2)=(2)(x+10)

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Solution for (x+4)(x+2)=(2)(x+10) equation: 


Simplifying
(x + 4)(x + 2) = (2)(x + 10)

Reorder the terms:
(4 + x)(x + 2) = (2)(x + 10)

Reorder the terms:
(4 + x)(2 + x) = (2)(x + 10)

Multiply (4 + x) * (2 + x)
(4(2 + x) + x(2 + x)) = (2)(x + 10)
((2 * 4 + x * 4) + x(2 + x)) = (2)(x + 10)
((8 + 4x) + x(2 + x)) = (2)(x + 10)
(8 + 4x + (2 * x + x * x)) = (2)(x + 10)
(8 + 4x + (2x + x2)) = (2)(x + 10)

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

Reorder the terms:
8 + 6x + x2 = 2(10 + x)
8 + 6x + x2 = (10 * 2 + x * 2)
8 + 6x + x2 = (20 + 2x)

Solving
8 + 6x + x2 = 20 + 2x

Solving for variable 'x'.

Reorder the terms:
8 + -20 + 6x + -2x + x2 = 20 + 2x + -20 + -2x

Combine like terms: 8 + -20 = -12
-12 + 6x + -2x + x2 = 20 + 2x + -20 + -2x

Combine like terms: 6x + -2x = 4x
-12 + 4x + x2 = 20 + 2x + -20 + -2x

Reorder the terms:
-12 + 4x + x2 = 20 + -20 + 2x + -2x

Combine like terms: 20 + -20 = 0
-12 + 4x + x2 = 0 + 2x + -2x
-12 + 4x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-12 + 4x + x2 = 0

Factor a trinomial.
(-6 + -1x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

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 = {-6, 2}

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