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

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


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

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

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

Multiply (-7 + y) * (4 + y)
-5y(-7(4 + y) + y(4 + y)) = 0
-5y((4 * -7 + y * -7) + y(4 + y)) = 0
-5y((-28 + -7y) + y(4 + y)) = 0
-5y(-28 + -7y + (4 * y + y * y)) = 0
-5y(-28 + -7y + (4y + y2)) = 0

Combine like terms: -7y + 4y = -3y
-5y(-28 + -3y + y2) = 0
(-28 * -5y + -3y * -5y + y2 * -5y) = 0
(140y + 15y2 + -5y3) = 0

Solving
140y + 15y2 + -5y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y'.
5y(28 + 3y + -1y2) = 0

Factor a trinomial.
5y((7 + -1y)(4 + 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 '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 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 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7

Subproblem 3
Set the factor '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

Solving
4 + y = 0

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

Add '-4' to each side of the equation.
4 + -4 + y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + y = 0 + -4
y = 0 + -4

Combine like terms: 0 + -4 = -4
y = -4

Simplifying
y = -4
Solution
y = {0, 7, -4}

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