y^2+5y-6=78

Solution for y^2+5y-6=78 equation:

Simplifying
y2 + 5y + -6 = 78

Reorder the terms:
-6 + 5y + y2 = 78

Solving
-6 + 5y + y2 = 78

Solving for variable 'y'.

Reorder the terms:
-6 + -78 + 5y + y2 = 78 + -78

Combine like terms: -6 + -78 = -84
-84 + 5y + y2 = 78 + -78

Combine like terms: 78 + -78 = 0
-84 + 5y + y2 = 0

Factor a trinomial.
(-12 + -1y)(7 + -1y) = 0

Subproblem 1
Set the factor '(-12 + -1y)' equal to zero and attempt to solve:

Simplifying
-12 + -1y = 0

Solving
-12 + -1y = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1y = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1y = 0 + 12
-1y = 0 + 12

Combine like terms: 0 + 12 = 12
-1y = 12

Divide each side by '-1'.
y = -12

Simplifying
y = -12
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 = {-12, 7}