0=2x^6+x^5-15x^4

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Solution for 0=2x^6+x^5-15x^4 equation: 


Simplifying
0 = 2x6 + x5 + -15x4

Reorder the terms:
0 = -15x4 + x5 + 2x6

Solving
0 = -15x4 + x5 + 2x6

Solving for variable 'x'.
Remove the zero:
15x4 + -1x5 + -2x6 = -15x4 + x5 + 2x6 + 15x4 + -1x5 + -2x6

Reorder the terms:
15x4 + -1x5 + -2x6 = -15x4 + 15x4 + x5 + -1x5 + 2x6 + -2x6

Combine like terms: -15x4 + 15x4 = 0
15x4 + -1x5 + -2x6 = 0 + x5 + -1x5 + 2x6 + -2x6
15x4 + -1x5 + -2x6 = x5 + -1x5 + 2x6 + -2x6

Combine like terms: x5 + -1x5 = 0
15x4 + -1x5 + -2x6 = 0 + 2x6 + -2x6
15x4 + -1x5 + -2x6 = 2x6 + -2x6

Combine like terms: 2x6 + -2x6 = 0
15x4 + -1x5 + -2x6 = 0

Factor out the Greatest Common Factor (GCF), 'x4'.
x4(15 + -1x + -2x2) = 0

Factor a trinomial.
x4((5 + -2x)(3 + x)) = 0


Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve:

Simplifying
x4 = 0

Solving
x4 = 0

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

Simplifying
x4 = 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 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {2.5, -3}

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