-3y(y+7)(y-5)=0

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Solution for -3y(y+7)(y-5)=0 equation: 


Simplifying
-3y(y + 7)(y + -5) = 0

Reorder the terms:
-3y(7 + y)(y + -5) = 0

Reorder the terms:
-3y(7 + y)(-5 + y) = 0

Multiply (7 + y) * (-5 + y)
-3y(7(-5 + y) + y(-5 + y)) = 0
-3y((-5 * 7 + y * 7) + y(-5 + y)) = 0
-3y((-35 + 7y) + y(-5 + y)) = 0
-3y(-35 + 7y + (-5 * y + y * y)) = 0
-3y(-35 + 7y + (-5y + y2)) = 0

Combine like terms: 7y + -5y = 2y
-3y(-35 + 2y + y2) = 0
(-35 * -3y + 2y * -3y + y2 * -3y) = 0
(105y + -6y2 + -3y3) = 0

Solving
105y + -6y2 + -3y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(35 + -2y + -1y2) = 0

Factor a trinomial.
3y((5 + -1y)(7 + y)) = 0

Ignore the factor 3.

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 '(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 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, 5, -7}

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