(8y^3+3y^2-8)+(7y^3+6y^2+8)=

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Solution for (8y^3+3y^2-8)+(7y^3+6y^2+8)= equation: 


Simplifying
(8y3 + 3y2 + -8) + (7y3 + 6y2 + 8) = 0

Reorder the terms:
(-8 + 3y2 + 8y3) + (7y3 + 6y2 + 8) = 0

Remove parenthesis around (-8 + 3y2 + 8y3)
-8 + 3y2 + 8y3 + (7y3 + 6y2 + 8) = 0

Reorder the terms:
-8 + 3y2 + 8y3 + (8 + 6y2 + 7y3) = 0

Remove parenthesis around (8 + 6y2 + 7y3)
-8 + 3y2 + 8y3 + 8 + 6y2 + 7y3 = 0

Reorder the terms:
-8 + 8 + 3y2 + 6y2 + 8y3 + 7y3 = 0

Combine like terms: -8 + 8 = 0
0 + 3y2 + 6y2 + 8y3 + 7y3 = 0
3y2 + 6y2 + 8y3 + 7y3 = 0

Combine like terms: 3y2 + 6y2 = 9y2
9y2 + 8y3 + 7y3 = 0

Combine like terms: 8y3 + 7y3 = 15y3
9y2 + 15y3 = 0

Solving
9y2 + 15y3 = 0

Solving for variable 'y'.

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

Ignore the factor 3.

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 '(3 + 5y)' equal to zero and attempt to solve:

Simplifying
3 + 5y = 0

Solving
3 + 5y = 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 + 5y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5y = 0 + -3
5y = 0 + -3

Combine like terms: 0 + -3 = -3
5y = -3

Divide each side by '5'.
y = -0.6

Simplifying
y = -0.6
Solution
y = {0, -0.6}

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