x(2x-2)=84

Solution for x(2x-2)=84 equation:

Simplifying
x(2x + -2) = 84

Reorder the terms:
x(-2 + 2x) = 84
(-2 * x + 2x * x) = 84
(-2x + 2x2) = 84

Solving
-2x + 2x2 = 84

Solving for variable 'x'.

Reorder the terms:
-84 + -2x + 2x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + -2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-42 + -1x + x2) = 0

Factor a trinomial.
2((-6 + -1x)(7 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-6, 7}