10y^6+34y^5+12y^4=0

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Solution for 10y^6+34y^5+12y^4=0 equation:


Simplifying
10y6 + 34y5 + 12y4 = 0

Reorder the terms:
12y4 + 34y5 + 10y6 = 0

Solving
12y4 + 34y5 + 10y6 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y4'.
2y4(6 + 17y + 5y2) = 0

Factor a trinomial.
2y4((3 + y)(2 + 5y)) = 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 '(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 '(2 + 5y)' equal to zero and attempt to solve: Simplifying 2 + 5y = 0 Solving 2 + 5y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5y = 0 + -2 5y = 0 + -2 Combine like terms: 0 + -2 = -2 5y = -2 Divide each side by '5'. y = -0.4 Simplifying y = -0.4

Solution

y = {-3, -0.4}

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