3(y+7)(-y-2)=0

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Solution for 3(y+7)(-y-2)=0 equation: 


Simplifying
3(y + 7)(-1y + -2) = 0

Reorder the terms:
3(7 + y)(-1y + -2) = 0

Reorder the terms:
3(7 + y)(-2 + -1y) = 0

Multiply (7 + y) * (-2 + -1y)
3(7(-2 + -1y) + y(-2 + -1y)) = 0
3((-2 * 7 + -1y * 7) + y(-2 + -1y)) = 0
3((-14 + -7y) + y(-2 + -1y)) = 0
3(-14 + -7y + (-2 * y + -1y * y)) = 0
3(-14 + -7y + (-2y + -1y2)) = 0

Combine like terms: -7y + -2y = -9y
3(-14 + -9y + -1y2) = 0
(-14 * 3 + -9y * 3 + -1y2 * 3) = 0
(-42 + -27y + -3y2) = 0

Solving
-42 + -27y + -3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(14 + 9y + y2) = 0

Factor a trinomial.
-3((7 + y)(2 + y)) = 0

Ignore the factor -3.

Subproblem 1
Set the factor '(7 + y)' equal to zero and attempt to solve:

Simplifying
7 + y = 0

Solving
7 + y = 0

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

Add '-7' to each side of the equation.
7 + -7 + y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + y = 0 + -7
y = 0 + -7

Combine like terms: 0 + -7 = -7
y = -7

Simplifying
y = -7

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 = {-7, -2}

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