x^2=84-8x

Solution for x^2=84-8x equation:

Simplifying
x2 = 84 + -8x

Solving
x2 = 84 + -8x

Solving for variable 'x'.

Reorder the terms:
-84 + 8x + x2 = 84 + -8x + -84 + 8x

Reorder the terms:
-84 + 8x + x2 = 84 + -84 + -8x + 8x

Combine like terms: 84 + -84 = 0
-84 + 8x + x2 = 0 + -8x + 8x
-84 + 8x + x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-84 + 8x + x2 = 0

Factor a trinomial.
(-14 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve:

Simplifying
-14 + -1x = 0

Solving
-14 + -1x = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1x = 0 + 14
-1x = 0 + 14

Combine like terms: 0 + 14 = 14
-1x = 14

Divide each side by '-1'.
x = -14

Simplifying
x = -14
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-14, 6}