-5(y-4)(-y+1)=0

Solution for -5(y-4)(-y+1)=0 equation:

Simplifying
-5(y + -4)(-1y + 1) = 0

Reorder the terms:
-5(-4 + y)(-1y + 1) = 0

Reorder the terms:
-5(-4 + y)(1 + -1y) = 0

Multiply (-4 + y) * (1 + -1y)
-5(-4(1 + -1y) + y(1 + -1y)) = 0
-5((1 * -4 + -1y * -4) + y(1 + -1y)) = 0
-5((-4 + 4y) + y(1 + -1y)) = 0
-5(-4 + 4y + (1 * y + -1y * y)) = 0
-5(-4 + 4y + (1y + -1y2)) = 0

Combine like terms: 4y + 1y = 5y
-5(-4 + 5y + -1y2) = 0
(-4 * -5 + 5y * -5 + -1y2 * -5) = 0
(20 + -25y + 5y2) = 0

Solving
20 + -25y + 5y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5'.
5(4 + -5y + y2) = 0

Factor a trinomial.
5((1 + -1y)(4 + -1y)) = 0

Ignore the factor 5.
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}