(15-3y)(12+4y)=0

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Solution for (15-3y)(12+4y)=0 equation: 


Simplifying
(15 + -3y)(12 + 4y) = 0

Multiply (15 + -3y) * (12 + 4y)
(15(12 + 4y) + -3y * (12 + 4y)) = 0
((12 * 15 + 4y * 15) + -3y * (12 + 4y)) = 0
((180 + 60y) + -3y * (12 + 4y)) = 0
(180 + 60y + (12 * -3y + 4y * -3y)) = 0
(180 + 60y + (-36y + -12y2)) = 0

Combine like terms: 60y + -36y = 24y
(180 + 24y + -12y2) = 0

Solving
180 + 24y + -12y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '12'.
12(15 + 2y + -1y2) = 0

Factor a trinomial.
12((5 + -1y)(3 + y)) = 0

Ignore the factor 12.

Subproblem 1
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

Subproblem 2
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

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

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

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

Simplifying
y = -3
Solution
y = {5, -3}

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