5y(y+7)(y+8)=0

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Solution for 5y(y+7)(y+8)=0 equation: 


Simplifying
5y(y + 7)(y + 8) = 0

Reorder the terms:
5y(7 + y)(y + 8) = 0

Reorder the terms:
5y(7 + y)(8 + y) = 0

Multiply (7 + y) * (8 + y)
5y(7(8 + y) + y(8 + y)) = 0
5y((8 * 7 + y * 7) + y(8 + y)) = 0
5y((56 + 7y) + y(8 + y)) = 0
5y(56 + 7y + (8 * y + y * y)) = 0
5y(56 + 7y + (8y + y2)) = 0

Combine like terms: 7y + 8y = 15y
5y(56 + 15y + y2) = 0
(56 * 5y + 15y * 5y + y2 * 5y) = 0
(280y + 75y2 + 5y3) = 0

Solving
280y + 75y2 + 5y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y'.
5y(56 + 15y + y2) = 0

Factor a trinomial.
5y((8 + y)(7 + y)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

Subproblem 2
Set the factor '(8 + y)' equal to zero and attempt to solve:

Simplifying
8 + y = 0

Solving
8 + y = 0

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

Add '-8' to each side of the equation.
8 + -8 + y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + y = 0 + -8
y = 0 + -8

Combine like terms: 0 + -8 = -8
y = -8

Simplifying
y = -8

Subproblem 3
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
Solution
y = {0, -8, -7}

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