-4y(y+7)(y+5)=0

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Solution for -4y(y+7)(y+5)=0 equation: 


Simplifying
-4y(y + 7)(y + 5) = 0

Reorder the terms:
-4y(7 + y)(y + 5) = 0

Reorder the terms:
-4y(7 + y)(5 + y) = 0

Multiply (7 + y) * (5 + y)
-4y(7(5 + y) + y(5 + y)) = 0
-4y((5 * 7 + y * 7) + y(5 + y)) = 0
-4y((35 + 7y) + y(5 + y)) = 0
-4y(35 + 7y + (5 * y + y * y)) = 0
-4y(35 + 7y + (5y + y2)) = 0

Combine like terms: 7y + 5y = 12y
-4y(35 + 12y + y2) = 0
(35 * -4y + 12y * -4y + y2 * -4y) = 0
(-140y + -48y2 + -4y3) = 0

Solving
-140y + -48y2 + -4y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '-4y'.
-4y(35 + 12y + y2) = 0

Factor a trinomial.
-4y((7 + y)(5 + y)) = 0

Ignore the factor -4.

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 '(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 3
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
Solution
y = {0, -7, -5}

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