x+2(x+5)=(x+12)x

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Solution for x+2(x+5)=(x+12)x equation: 


Simplifying
x + 2(x + 5) = (x + 12) * x

Reorder the terms:
x + 2(5 + x) = (x + 12) * x
x + (5 * 2 + x * 2) = (x + 12) * x
x + (10 + 2x) = (x + 12) * x

Reorder the terms:
10 + x + 2x = (x + 12) * x

Combine like terms: x + 2x = 3x
10 + 3x = (x + 12) * x

Reorder the terms:
10 + 3x = (12 + x) * x

Reorder the terms for easier multiplication:
10 + 3x = x(12 + x)
10 + 3x = (12 * x + x * x)
10 + 3x = (12x + x2)

Solving
10 + 3x = 12x + x2

Solving for variable 'x'.

Combine like terms: 3x + -12x = -9x
10 + -9x + -1x2 = 12x + x2 + -12x + -1x2

Reorder the terms:
10 + -9x + -1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
10 + -9x + -1x2 = 0 + x2 + -1x2
10 + -9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10 + -9x + -1x2 = 0

Factor a trinomial.
(1 + -1x)(10 + x) = 0


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

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Solution
x = {1, -10}

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