-3y(y-8)(2y+1)=0

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Solution for -3y(y-8)(2y+1)=0 equation: 


Simplifying
-3y(y + -8)(2y + 1) = 0

Reorder the terms:
-3y(-8 + y)(2y + 1) = 0

Reorder the terms:
-3y(-8 + y)(1 + 2y) = 0

Multiply (-8 + y) * (1 + 2y)
-3y(-8(1 + 2y) + y(1 + 2y)) = 0
-3y((1 * -8 + 2y * -8) + y(1 + 2y)) = 0
-3y((-8 + -16y) + y(1 + 2y)) = 0
-3y(-8 + -16y + (1 * y + 2y * y)) = 0
-3y(-8 + -16y + (1y + 2y2)) = 0

Combine like terms: -16y + 1y = -15y
-3y(-8 + -15y + 2y2) = 0
(-8 * -3y + -15y * -3y + 2y2 * -3y) = 0
(24y + 45y2 + -6y3) = 0

Solving
24y + 45y2 + -6y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(8 + 15y + -2y2) = 0

Factor a trinomial.
3y((8 + -1y)(1 + 2y)) = 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 '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y = 0 + -8
-1y = 0 + -8

Combine like terms: 0 + -8 = -8
-1y = -8

Divide each side by '-1'.
y = 8

Simplifying
y = 8

Subproblem 3
Set the factor '(1 + 2y)' equal to zero and attempt to solve:

Simplifying
1 + 2y = 0

Solving
1 + 2y = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2y = 0 + -1
2y = 0 + -1

Combine like terms: 0 + -1 = -1
2y = -1

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Solution
y = {0, 8, -0.5}

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