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

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

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

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

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

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

Combine like terms: 4y + -1y = 3y
4[(-4 + 3y + y2)] = 0
[-4 * 4 + 3y * 4 + y2 * 4] = 0
[-16 + 12y + 4y2] = 0

Solving
-16 + 12y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 3y + y2) = 0

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

Ignore the factor 4.
Subproblem 1
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
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 = {-4, 1}