x^2+20x-74=8x-10

Solution for x^2+20x-74=8x-10 equation:

Simplifying
x2 + 20x + -74 = 8x + -10

Reorder the terms:
-74 + 20x + x2 = 8x + -10

Reorder the terms:
-74 + 20x + x2 = -10 + 8x

Solving
-74 + 20x + x2 = -10 + 8x

Solving for variable 'x'.

Reorder the terms:
-74 + 10 + 20x + -8x + x2 = -10 + 8x + 10 + -8x

Combine like terms: -74 + 10 = -64
-64 + 20x + -8x + x2 = -10 + 8x + 10 + -8x

Combine like terms: 20x + -8x = 12x
-64 + 12x + x2 = -10 + 8x + 10 + -8x

Reorder the terms:
-64 + 12x + x2 = -10 + 10 + 8x + -8x

Combine like terms: -10 + 10 = 0
-64 + 12x + x2 = 0 + 8x + -8x
-64 + 12x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-64 + 12x + x2 = 0

Factor a trinomial.
(-16 + -1x)(4 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-16, 4}