(y+4)(y-1)=14

Solution for (y+4)(y-1)=14 equation:

Simplifying
(y + 4)(y + -1) = 14

Reorder the terms:
(4 + y)(y + -1) = 14

Reorder the terms:
(4 + y)(-1 + y) = 14

Multiply (4 + y) * (-1 + y)
(4(-1 + y) + y(-1 + y)) = 14
((-1 * 4 + y * 4) + y(-1 + y)) = 14
((-4 + 4y) + y(-1 + y)) = 14
(-4 + 4y + (-1 * y + y * y)) = 14
(-4 + 4y + (-1y + y2)) = 14

Combine like terms: 4y + -1y = 3y
(-4 + 3y + y2) = 14

Solving
-4 + 3y + y2 = 14

Solving for variable 'y'.

Reorder the terms:
-4 + -14 + 3y + y2 = 14 + -14

Combine like terms: -4 + -14 = -18
-18 + 3y + y2 = 14 + -14

Combine like terms: 14 + -14 = 0
-18 + 3y + y2 = 0

Factor a trinomial.
(-6 + -1y)(3 + -1y) = 0

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 '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-6, 3}