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

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

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

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

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

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

Combine like terms: 5y + 1y = 6y
4(-5 + 6y + -1y2) = 0
(-5 * 4 + 6y * 4 + -1y2 * 4) = 0
(-20 + 24y + -4y2) = 0

Solving
-20 + 24y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 6y + -1y2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + y)' equal to zero and attempt to solve:

Simplifying
-5 + y = 0

Solving
-5 + y = 0

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

Add '5' to each side of the equation.
-5 + 5 + y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + y = 0 + 5
y = 0 + 5

Combine like terms: 0 + 5 = 5
y = 5

Simplifying
y = 5
Subproblem 2
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
Solution
y = {5, 1}