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

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


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

Reorder the terms:
x(12 + x) = x + 2(x + 5)
(12 * x + x * x) = x + 2(x + 5)
(12x + x2) = x + 2(x + 5)

Reorder the terms:
12x + x2 = x + 2(5 + x)
12x + x2 = x + (5 * 2 + x * 2)
12x + x2 = x + (10 + 2x)

Reorder the terms:
12x + x2 = 10 + x + 2x

Combine like terms: x + 2x = 3x
12x + x2 = 10 + 3x

Solving
12x + x2 = 10 + 3x

Solving for variable 'x'.

Reorder the terms:
-10 + 12x + -3x + x2 = 10 + 3x + -10 + -3x

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

Reorder the terms:
-10 + 9x + x2 = 10 + -10 + 3x + -3x

Combine like terms: 10 + -10 = 0
-10 + 9x + x2 = 0 + 3x + -3x
-10 + 9x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-10 + 9x + x2 = 0

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


Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 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 + -1x = 0 + 10

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

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

Divide each side by '-1'.
x = -10

Simplifying
x = -10

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 = {-10, 1}

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