x^2+2x-62=3x-6

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Solution for x^2+2x-62=3x-6 equation: 


Simplifying
x2 + 2x + -62 = 3x + -6

Reorder the terms:
-62 + 2x + x2 = 3x + -6

Reorder the terms:
-62 + 2x + x2 = -6 + 3x

Solving
-62 + 2x + x2 = -6 + 3x

Solving for variable 'x'.

Reorder the terms:
-62 + 6 + 2x + -3x + x2 = -6 + 3x + 6 + -3x

Combine like terms: -62 + 6 = -56
-56 + 2x + -3x + x2 = -6 + 3x + 6 + -3x

Combine like terms: 2x + -3x = -1x
-56 + -1x + x2 = -6 + 3x + 6 + -3x

Reorder the terms:
-56 + -1x + x2 = -6 + 6 + 3x + -3x

Combine like terms: -6 + 6 = 0
-56 + -1x + x2 = 0 + 3x + -3x
-56 + -1x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-56 + -1x + x2 = 0

Factor a trinomial.
(-7 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

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 = {-7, 8}

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