(y-4)(y+1)=0

Solution for (y-4)(y+1)=0 equation:

Simplifying
(y + -4)(y + 1) = 0

Reorder the terms:
(-4 + y)(y + 1) = 0

Reorder the terms:
(-4 + y)(1 + y) = 0

Multiply (-4 + y) * (1 + y)
(-4(1 + y) + y(1 + y)) = 0
((1 * -4 + y * -4) + y(1 + y)) = 0
((-4 + -4y) + y(1 + y)) = 0
(-4 + -4y + (1 * y + y * y)) = 0
(-4 + -4y + (1y + y2)) = 0

Combine like terms: -4y + 1y = -3y
(-4 + -3y + y2) = 0

Solving
-4 + -3y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -1y)(4 + -1y) = 0

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

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 0

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

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

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

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

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

Simplifying
y = -1
Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {-1, 4}