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

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


Simplifying
3(y + 2)(-1y + -5) = 0

Reorder the terms:
3(2 + y)(-1y + -5) = 0

Reorder the terms:
3(2 + y)(-5 + -1y) = 0

Multiply (2 + y) * (-5 + -1y)
3(2(-5 + -1y) + y(-5 + -1y)) = 0
3((-5 * 2 + -1y * 2) + y(-5 + -1y)) = 0
3((-10 + -2y) + y(-5 + -1y)) = 0
3(-10 + -2y + (-5 * y + -1y * y)) = 0
3(-10 + -2y + (-5y + -1y2)) = 0

Combine like terms: -2y + -5y = -7y
3(-10 + -7y + -1y2) = 0
(-10 * 3 + -7y * 3 + -1y2 * 3) = 0
(-30 + -21y + -3y2) = 0

Solving
-30 + -21y + -3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(10 + 7y + y2) = 0

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

Ignore the factor -3.

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 '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

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

Add '-2' to each side of the equation.
2 + -2 + y = 0 + -2

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

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

Simplifying
y = -2
Solution
y = {-5, -2}

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