4(y-5)(2y+3)=0

Solution for 4(y-5)(2y+3)=0 equation:

Simplifying
4(y + -5)(2y + 3) = 0

Reorder the terms:
4(-5 + y)(2y + 3) = 0

Reorder the terms:
4(-5 + y)(3 + 2y) = 0

Multiply (-5 + y) * (3 + 2y)
4(-5(3 + 2y) + y(3 + 2y)) = 0
4((3 * -5 + 2y * -5) + y(3 + 2y)) = 0
4((-15 + -10y) + y(3 + 2y)) = 0
4(-15 + -10y + (3 * y + 2y * y)) = 0
4(-15 + -10y + (3y + 2y2)) = 0

Combine like terms: -10y + 3y = -7y
4(-15 + -7y + 2y2) = 0
(-15 * 4 + -7y * 4 + 2y2 * 4) = 0
(-60 + -28y + 8y2) = 0

Solving
-60 + -28y + 8y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + -7y + 2y2) = 0

Factor a trinomial.
4((-3 + -2y)(5 + -1y)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + -2y)' equal to zero and attempt to solve:

Simplifying
-3 + -2y = 0

Solving
-3 + -2y = 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 + -2y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2y = 0 + 3
-2y = 0 + 3

Combine like terms: 0 + 3 = 3
-2y = 3

Divide each side by '-2'.
y = -1.5

Simplifying
y = -1.5
Subproblem 2
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 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 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {-1.5, 5}