x^2-11x-53=-3x-5

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Solution for x^2-11x-53=-3x-5 equation: 


Simplifying
x2 + -11x + -53 = -3x + -5

Reorder the terms:
-53 + -11x + x2 = -3x + -5

Reorder the terms:
-53 + -11x + x2 = -5 + -3x

Solving
-53 + -11x + x2 = -5 + -3x

Solving for variable 'x'.

Reorder the terms:
-53 + 5 + -11x + 3x + x2 = -5 + -3x + 5 + 3x

Combine like terms: -53 + 5 = -48
-48 + -11x + 3x + x2 = -5 + -3x + 5 + 3x

Combine like terms: -11x + 3x = -8x
-48 + -8x + x2 = -5 + -3x + 5 + 3x

Reorder the terms:
-48 + -8x + x2 = -5 + 5 + -3x + 3x

Combine like terms: -5 + 5 = 0
-48 + -8x + x2 = 0 + -3x + 3x
-48 + -8x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-48 + -8x + x2 = 0

Factor a trinomial.
(-4 + -1x)(12 + -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 '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-4, 12}

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