0=10y^7+45y^6+45y^5

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Solution for 0=10y^7+45y^6+45y^5 equation: 


Simplifying
0 = 10y7 + 45y6 + 45y5

Reorder the terms:
0 = 45y5 + 45y6 + 10y7

Solving
0 = 45y5 + 45y6 + 10y7

Solving for variable 'y'.
Remove the zero:
-45y5 + -45y6 + -10y7 = 45y5 + 45y6 + 10y7 + -45y5 + -45y6 + -10y7

Reorder the terms:
-45y5 + -45y6 + -10y7 = 45y5 + -45y5 + 45y6 + -45y6 + 10y7 + -10y7

Combine like terms: 45y5 + -45y5 = 0
-45y5 + -45y6 + -10y7 = 0 + 45y6 + -45y6 + 10y7 + -10y7
-45y5 + -45y6 + -10y7 = 45y6 + -45y6 + 10y7 + -10y7

Combine like terms: 45y6 + -45y6 = 0
-45y5 + -45y6 + -10y7 = 0 + 10y7 + -10y7
-45y5 + -45y6 + -10y7 = 10y7 + -10y7

Combine like terms: 10y7 + -10y7 = 0
-45y5 + -45y6 + -10y7 = 0

Factor out the Greatest Common Factor (GCF), '-5y5'.
-5y5(9 + 9y + 2y2) = 0

Factor a trinomial.
-5y5((3 + y)(3 + 2y)) = 0

Ignore the factor -5.

Subproblem 1
Set the factor 'y5' equal to zero and attempt to solve:

Simplifying
y5 = 0

Solving
y5 = 0

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

Simplifying
y5 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
3 + y = 0

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

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

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

Simplifying
y = -3

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

Simplifying
3 + 2y = 0

Solving
3 + 2y = 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 + 2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2y = 0 + -3
2y = 0 + -3

Combine like terms: 0 + -3 = -3
2y = -3

Divide each side by '2'.
y = -1.5

Simplifying
y = -1.5
Solution
y = {-3, -1.5}

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