x^2+7x-82=5x-2

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Solution for x^2+7x-82=5x-2 equation: 


Simplifying
x2 + 7x + -82 = 5x + -2

Reorder the terms:
-82 + 7x + x2 = 5x + -2

Reorder the terms:
-82 + 7x + x2 = -2 + 5x

Solving
-82 + 7x + x2 = -2 + 5x

Solving for variable 'x'.

Reorder the terms:
-82 + 2 + 7x + -5x + x2 = -2 + 5x + 2 + -5x

Combine like terms: -82 + 2 = -80
-80 + 7x + -5x + x2 = -2 + 5x + 2 + -5x

Combine like terms: 7x + -5x = 2x
-80 + 2x + x2 = -2 + 5x + 2 + -5x

Reorder the terms:
-80 + 2x + x2 = -2 + 2 + 5x + -5x

Combine like terms: -2 + 2 = 0
-80 + 2x + x2 = 0 + 5x + -5x
-80 + 2x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-80 + 2x + x2 = 0

Factor a trinomial.
(-10 + -1x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-10, 8}

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