x^2-10x-45=-6

Solution for x^2-10x-45=-6 equation:

Simplifying
x2 + -10x + -45 = -6

Reorder the terms:
-45 + -10x + x2 = -6

Solving
-45 + -10x + x2 = -6

Solving for variable 'x'.

Reorder the terms:
-45 + 6 + -10x + x2 = -6 + 6

Combine like terms: -45 + 6 = -39
-39 + -10x + x2 = -6 + 6

Combine like terms: -6 + 6 = 0
-39 + -10x + x2 = 0

Factor a trinomial.
(-3 + -1x)(13 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {-3, 13}