0=x(x+13)+40

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Solution for 0=x(x+13)+40 equation: 


Simplifying
0 = x(x + 13) + 40

Reorder the terms:
0 = x(13 + x) + 40
0 = (13 * x + x * x) + 40
0 = (13x + x2) + 40

Reorder the terms:
0 = 40 + 13x + x2

Solving
0 = 40 + 13x + x2

Solving for variable 'x'.

Combine like terms: 0 + -40 = -40
-40 + -13x + -1x2 = 40 + 13x + x2 + -40 + -13x + -1x2

Reorder the terms:
-40 + -13x + -1x2 = 40 + -40 + 13x + -13x + x2 + -1x2

Combine like terms: 40 + -40 = 0
-40 + -13x + -1x2 = 0 + 13x + -13x + x2 + -1x2
-40 + -13x + -1x2 = 13x + -13x + x2 + -1x2

Combine like terms: 13x + -13x = 0
-40 + -13x + -1x2 = 0 + x2 + -1x2
-40 + -13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-40 + -13x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(40 + 13x + x2) = 0

Factor a trinomial.
-1((8 + x)(5 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8

Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {-8, -5}

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