16y(y^2+3)=-32y(y-2)-31y

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Solution for 16y(y^2+3)=-32y(y-2)-31y equation: 


Simplifying
16y(y2 + 3) = -32y(y + -2) + -31y

Reorder the terms:
16y(3 + y2) = -32y(y + -2) + -31y
(3 * 16y + y2 * 16y) = -32y(y + -2) + -31y
(48y + 16y3) = -32y(y + -2) + -31y

Reorder the terms:
48y + 16y3 = -32y(-2 + y) + -31y
48y + 16y3 = (-2 * -32y + y * -32y) + -31y
48y + 16y3 = (64y + -32y2) + -31y

Reorder the terms:
48y + 16y3 = 64y + -31y + -32y2

Combine like terms: 64y + -31y = 33y
48y + 16y3 = 33y + -32y2

Solving
48y + 16y3 = 33y + -32y2

Solving for variable 'y'.

Reorder the terms:
48y + -33y + 32y2 + 16y3 = 33y + -32y2 + -33y + 32y2

Combine like terms: 48y + -33y = 15y
15y + 32y2 + 16y3 = 33y + -32y2 + -33y + 32y2

Reorder the terms:
15y + 32y2 + 16y3 = 33y + -33y + -32y2 + 32y2

Combine like terms: 33y + -33y = 0
15y + 32y2 + 16y3 = 0 + -32y2 + 32y2
15y + 32y2 + 16y3 = -32y2 + 32y2

Combine like terms: -32y2 + 32y2 = 0
15y + 32y2 + 16y3 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(15 + 32y + 16y2) = 0

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


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 + 4y)' equal to zero and attempt to solve:

Simplifying
5 + 4y = 0

Solving
5 + 4y = 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 + 4y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4y = 0 + -5
4y = 0 + -5

Combine like terms: 0 + -5 = -5
4y = -5

Divide each side by '4'.
y = -1.25

Simplifying
y = -1.25

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

Simplifying
3 + 4y = 0

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

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

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

Divide each side by '4'.
y = -0.75

Simplifying
y = -0.75
Solution
y = {0, -1.25, -0.75}

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