(y+6)(y-1)=78

Solution for (y+6)(y-1)=78 equation:

Simplifying
(y + 6)(y + -1) = 78

Reorder the terms:
(6 + y)(y + -1) = 78

Reorder the terms:
(6 + y)(-1 + y) = 78

Multiply (6 + y) * (-1 + y)
(6(-1 + y) + y(-1 + y)) = 78
((-1 * 6 + y * 6) + y(-1 + y)) = 78
((-6 + 6y) + y(-1 + y)) = 78
(-6 + 6y + (-1 * y + y * y)) = 78
(-6 + 6y + (-1y + y2)) = 78

Combine like terms: 6y + -1y = 5y
(-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}