x^2+12x-13=4x+7

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Solution for x^2+12x-13=4x+7 equation: 


Simplifying
x2 + 12x + -13 = 4x + 7

Reorder the terms:
-13 + 12x + x2 = 4x + 7

Reorder the terms:
-13 + 12x + x2 = 7 + 4x

Solving
-13 + 12x + x2 = 7 + 4x

Solving for variable 'x'.

Reorder the terms:
-13 + -7 + 12x + -4x + x2 = 7 + 4x + -7 + -4x

Combine like terms: -13 + -7 = -20
-20 + 12x + -4x + x2 = 7 + 4x + -7 + -4x

Combine like terms: 12x + -4x = 8x
-20 + 8x + x2 = 7 + 4x + -7 + -4x

Reorder the terms:
-20 + 8x + x2 = 7 + -7 + 4x + -4x

Combine like terms: 7 + -7 = 0
-20 + 8x + x2 = 0 + 4x + -4x
-20 + 8x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-20 + 8x + x2 = 0

Factor a trinomial.
(-10 + -1x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-10, 2}

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