(25+y)(4y-12)=0

Solution for (25+y)(4y-12)=0 equation:

Simplifying
(25 + y)(4y + -12) = 0

Reorder the terms:
(25 + y)(-12 + 4y) = 0

Multiply (25 + y) * (-12 + 4y)
(25(-12 + 4y) + y(-12 + 4y)) = 0
((-12 * 25 + 4y * 25) + y(-12 + 4y)) = 0
((-300 + 100y) + y(-12 + 4y)) = 0
(-300 + 100y + (-12 * y + 4y * y)) = 0
(-300 + 100y + (-12y + 4y2)) = 0

Combine like terms: 100y + -12y = 88y
(-300 + 88y + 4y2) = 0

Solving
-300 + 88y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-75 + 22y + y2) = 0

Factor a trinomial.
4((-25 + -1y)(3 + -1y)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-25 + -1y)' equal to zero and attempt to solve:

Simplifying
-25 + -1y = 0

Solving
-25 + -1y = 0

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

Add '25' to each side of the equation.
-25 + 25 + -1y = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1y = 0 + 25
-1y = 0 + 25

Combine like terms: 0 + 25 = 25
-1y = 25

Divide each side by '-1'.
y = -25

Simplifying
y = -25
Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-25, 3}