2y^2-2y=84

Solution for 2y^2-2y=84 equation:

Simplifying
2y2 + -2y = 84

Reorder the terms:
-2y + 2y2 = 84

Solving
-2y + 2y2 = 84

Solving for variable 'y'.

Reorder the terms:
-84 + -2y + 2y2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + -2y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-42 + -1y + y2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -1y)' equal to zero and attempt to solve:

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 0

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

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

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

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

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

Simplifying
y = -6
Subproblem 2
Set the factor '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 0

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

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

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

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

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

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