x^2-13x-67=-3x-11

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Solution for x^2-13x-67=-3x-11 equation: 


Simplifying
x2 + -13x + -67 = -3x + -11

Reorder the terms:
-67 + -13x + x2 = -3x + -11

Reorder the terms:
-67 + -13x + x2 = -11 + -3x

Solving
-67 + -13x + x2 = -11 + -3x

Solving for variable 'x'.

Reorder the terms:
-67 + 11 + -13x + 3x + x2 = -11 + -3x + 11 + 3x

Combine like terms: -67 + 11 = -56
-56 + -13x + 3x + x2 = -11 + -3x + 11 + 3x

Combine like terms: -13x + 3x = -10x
-56 + -10x + x2 = -11 + -3x + 11 + 3x

Reorder the terms:
-56 + -10x + x2 = -11 + 11 + -3x + 3x

Combine like terms: -11 + 11 = 0
-56 + -10x + x2 = 0 + -3x + 3x
-56 + -10x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-56 + -10x + x2 = 0

Factor a trinomial.
(-4 + -1x)(14 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {-4, 14}

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