x^2+13x-38=5x-5

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Solution for x^2+13x-38=5x-5 equation: 


Simplifying
x2 + 13x + -38 = 5x + -5

Reorder the terms:
-38 + 13x + x2 = 5x + -5

Reorder the terms:
-38 + 13x + x2 = -5 + 5x

Solving
-38 + 13x + x2 = -5 + 5x

Solving for variable 'x'.

Reorder the terms:
-38 + 5 + 13x + -5x + x2 = -5 + 5x + 5 + -5x

Combine like terms: -38 + 5 = -33
-33 + 13x + -5x + x2 = -5 + 5x + 5 + -5x

Combine like terms: 13x + -5x = 8x
-33 + 8x + x2 = -5 + 5x + 5 + -5x

Reorder the terms:
-33 + 8x + x2 = -5 + 5 + 5x + -5x

Combine like terms: -5 + 5 = 0
-33 + 8x + x2 = 0 + 5x + -5x
-33 + 8x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-33 + 8x + x2 = 0

Factor a trinomial.
(-11 + -1x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11

Subproblem 2
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
Solution
x = {-11, 3}

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