x^2-10x-31=-3x-1

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Solution for x^2-10x-31=-3x-1 equation: 


Simplifying
x2 + -10x + -31 = -3x + -1

Reorder the terms:
-31 + -10x + x2 = -3x + -1

Reorder the terms:
-31 + -10x + x2 = -1 + -3x

Solving
-31 + -10x + x2 = -1 + -3x

Solving for variable 'x'.

Reorder the terms:
-31 + 1 + -10x + 3x + x2 = -1 + -3x + 1 + 3x

Combine like terms: -31 + 1 = -30
-30 + -10x + 3x + x2 = -1 + -3x + 1 + 3x

Combine like terms: -10x + 3x = -7x
-30 + -7x + x2 = -1 + -3x + 1 + 3x

Reorder the terms:
-30 + -7x + x2 = -1 + 1 + -3x + 3x

Combine like terms: -1 + 1 = 0
-30 + -7x + x2 = 0 + -3x + 3x
-30 + -7x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-30 + -7x + x2 = 0

Factor a trinomial.
(-3 + -1x)(10 + -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 '(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
Solution
x = {-3, 10}

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