=4y^6+22y^5+10y^4

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Solution for =4y^6+22y^5+10y^4 equation: 


Simplifying
0 = 4y6 + 22y5 + 10y4

Reorder the terms:
0 = 10y4 + 22y5 + 4y6

Solving
0 = 10y4 + 22y5 + 4y6

Solving for variable 'y'.
Remove the zero:
-10y4 + -22y5 + -4y6 = 10y4 + 22y5 + 4y6 + -10y4 + -22y5 + -4y6

Reorder the terms:
-10y4 + -22y5 + -4y6 = 10y4 + -10y4 + 22y5 + -22y5 + 4y6 + -4y6

Combine like terms: 10y4 + -10y4 = 0
-10y4 + -22y5 + -4y6 = 0 + 22y5 + -22y5 + 4y6 + -4y6
-10y4 + -22y5 + -4y6 = 22y5 + -22y5 + 4y6 + -4y6

Combine like terms: 22y5 + -22y5 = 0
-10y4 + -22y5 + -4y6 = 0 + 4y6 + -4y6
-10y4 + -22y5 + -4y6 = 4y6 + -4y6

Combine like terms: 4y6 + -4y6 = 0
-10y4 + -22y5 + -4y6 = 0

Factor out the Greatest Common Factor (GCF), '-2y4'.
-2y4(5 + 11y + 2y2) = 0

Factor a trinomial.
-2y4((5 + y)(1 + 2y)) = 0

Ignore the factor -2.

Subproblem 1
Set the factor 'y4' equal to zero and attempt to solve:

Simplifying
y4 = 0

Solving
y4 = 0

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

Simplifying
y4 = 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 '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

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

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

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

Simplifying
y = -5

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 = {-5, -0.5}

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