5y^2(3y+4)(y-4)=

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Solution for 5y^2(3y+4)(y-4)= equation: 


Simplifying
5y2(3y + 4)(y + -4) = 0

Reorder the terms:
5y2(4 + 3y)(y + -4) = 0

Reorder the terms:
5y2(4 + 3y)(-4 + y) = 0

Multiply (4 + 3y) * (-4 + y)
5y2(4(-4 + y) + 3y * (-4 + y)) = 0
5y2((-4 * 4 + y * 4) + 3y * (-4 + y)) = 0
5y2((-16 + 4y) + 3y * (-4 + y)) = 0
5y2(-16 + 4y + (-4 * 3y + y * 3y)) = 0
5y2(-16 + 4y + (-12y + 3y2)) = 0

Combine like terms: 4y + -12y = -8y
5y2(-16 + -8y + 3y2) = 0
(-16 * 5y2 + -8y * 5y2 + 3y2 * 5y2) = 0
(-80y2 + -40y3 + 15y4) = 0

Solving
-80y2 + -40y3 + 15y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y2'.
5y2(-16 + -8y + 3y2) = 0

Factor a trinomial.
5y2((-4 + -3y)(4 + -1y)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Simplifying
y2 = 0

Take the square root of each side:
y = {0}

Subproblem 2
Set the factor '(-4 + -3y)' equal to zero and attempt to solve:

Simplifying
-4 + -3y = 0

Solving
-4 + -3y = 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 + -3y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3y = 0 + 4
-3y = 0 + 4

Combine like terms: 0 + 4 = 4
-3y = 4

Divide each side by '-3'.
y = -1.333333333

Simplifying
y = -1.333333333

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, -1.333333333, 4}

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