5y(y-4)(y+3)=0

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Solution for 5y(y-4)(y+3)=0 equation: 


Simplifying
5y(y + -4)(y + 3) = 0

Reorder the terms:
5y(-4 + y)(y + 3) = 0

Reorder the terms:
5y(-4 + y)(3 + y) = 0

Multiply (-4 + y) * (3 + y)
5y(-4(3 + y) + y(3 + y)) = 0
5y((3 * -4 + y * -4) + y(3 + y)) = 0
5y((-12 + -4y) + y(3 + y)) = 0
5y(-12 + -4y + (3 * y + y * y)) = 0
5y(-12 + -4y + (3y + y2)) = 0

Combine like terms: -4y + 3y = -1y
5y(-12 + -1y + y2) = 0
(-12 * 5y + -1y * 5y + y2 * 5y) = 0
(-60y + -5y2 + 5y3) = 0

Solving
-60y + -5y2 + 5y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y'.
5y(-12 + -1y + y2) = 0

Factor a trinomial.
5y((-3 + -1y)(4 + -1y)) = 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 '(-3 + -1y)' equal to zero and attempt to solve:

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3

Subproblem 3
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 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 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {0, -3, 4}

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