7y^2+28y-84=0

Solution for 7y^2+28y-84=0 equation:

Simplifying
7y2 + 28y + -84 = 0

Reorder the terms:
-84 + 28y + 7y2 = 0

Solving
-84 + 28y + 7y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-12 + 4y + y2) = 0

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

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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-6, 2}