x^2-x-53=3

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

Simplifying
x2 + -1x + -53 = 3

Reorder the terms:
-53 + -1x + x2 = 3

Solving
-53 + -1x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
-53 + -3 + -1x + x2 = 3 + -3

Combine like terms: -53 + -3 = -56
-56 + -1x + x2 = 3 + -3

Combine like terms: 3 + -3 = 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}