x^2-12x-54=10

Solution for x^2-12x-54=10 equation:

Simplifying
x2 + -12x + -54 = 10

Reorder the terms:
-54 + -12x + x2 = 10

Solving
-54 + -12x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
-54 + -10 + -12x + x2 = 10 + -10

Combine like terms: -54 + -10 = -64
-64 + -12x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-64 + -12x + x2 = 0

Factor a trinomial.
(-4 + -1x)(16 + -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 '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {-4, 16}