x^2-16x-61=-4

Solution for x^2-16x-61=-4 equation:

Simplifying
x2 + -16x + -61 = -4

Reorder the terms:
-61 + -16x + x2 = -4

Solving
-61 + -16x + x2 = -4

Solving for variable 'x'.

Reorder the terms:
-61 + 4 + -16x + x2 = -4 + 4

Combine like terms: -61 + 4 = -57
-57 + -16x + x2 = -4 + 4

Combine like terms: -4 + 4 = 0
-57 + -16x + x2 = 0

Factor a trinomial.
(-3 + -1x)(19 + -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 '(19 + -1x)' equal to zero and attempt to solve:

Simplifying
19 + -1x = 0

Solving
19 + -1x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1x = 0 + -19
-1x = 0 + -19

Combine like terms: 0 + -19 = -19
-1x = -19

Divide each side by '-1'.
x = 19

Simplifying
x = 19
Solution
x = {-3, 19}