x(x+2)=31+7(x+x+2)

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Solution for x(x+2)=31+7(x+x+2) equation: 


Simplifying
x(x + 2) = 31 + 7(x + x + 2)

Reorder the terms:
x(2 + x) = 31 + 7(x + x + 2)
(2 * x + x * x) = 31 + 7(x + x + 2)
(2x + x2) = 31 + 7(x + x + 2)

Reorder the terms:
2x + x2 = 31 + 7(2 + x + x)

Combine like terms: x + x = 2x
2x + x2 = 31 + 7(2 + 2x)
2x + x2 = 31 + (2 * 7 + 2x * 7)
2x + x2 = 31 + (14 + 14x)

Combine like terms: 31 + 14 = 45
2x + x2 = 45 + 14x

Solving
2x + x2 = 45 + 14x

Solving for variable 'x'.

Reorder the terms:
-45 + 2x + -14x + x2 = 45 + 14x + -45 + -14x

Combine like terms: 2x + -14x = -12x
-45 + -12x + x2 = 45 + 14x + -45 + -14x

Reorder the terms:
-45 + -12x + x2 = 45 + -45 + 14x + -14x

Combine like terms: 45 + -45 = 0
-45 + -12x + x2 = 0 + 14x + -14x
-45 + -12x + x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-45 + -12x + x2 = 0

Factor a trinomial.
(-3 + -1x)(15 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {-3, 15}

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