2=x^2+13x+32

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Solution for 2=x^2+13x+32 equation: 


Simplifying
2 = x2 + 13x + 32

Reorder the terms:
2 = 32 + 13x + x2

Solving
2 = 32 + 13x + x2

Solving for variable 'x'.

Combine like terms: 2 + -32 = -30
-30 + -13x + -1x2 = 32 + 13x + x2 + -32 + -13x + -1x2

Reorder the terms:
-30 + -13x + -1x2 = 32 + -32 + 13x + -13x + x2 + -1x2

Combine like terms: 32 + -32 = 0
-30 + -13x + -1x2 = 0 + 13x + -13x + x2 + -1x2
-30 + -13x + -1x2 = 13x + -13x + x2 + -1x2

Combine like terms: 13x + -13x = 0
-30 + -13x + -1x2 = 0 + x2 + -1x2
-30 + -13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-30 + -13x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(30 + 13x + x2) = 0

Factor a trinomial.
-1((10 + x)(3 + x)) = 0

Ignore the factor -1.

Subproblem 1
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

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {-10, -3}

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