y^5-10y^3+9y=0

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Solution for y^5-10y^3+9y=0 equation:


Simplifying
y5 + -10y3 + 9y = 0

Reorder the terms:
9y + -10y3 + y5 = 0

Solving
9y + -10y3 + y5 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(9 + -10y2 + y4) = 0

Factor a trinomial.
y((1 + -1y2)(9 + -1y2)) = 0

Factor a difference between two squares.
y(((1 + y)(1 + -1y))(9 + -1y2)) = 0

Factor a difference between two squares.
y(((3 + y)(3 + -1y))(1 + y)(1 + -1y)) = 0

Subproblem 1

Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0

Subproblem 2

Set the factor '(1 + y)' equal to zero and attempt to solve: Simplifying 1 + y = 0 Solving 1 + y = 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 + y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + y = 0 + -1 y = 0 + -1 Combine like terms: 0 + -1 = -1 y = -1 Simplifying y = -1

Subproblem 3

Set the factor '(1 + -1y)' equal to zero and attempt to solve: Simplifying 1 + -1y = 0 Solving 1 + -1y = 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 + -1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1y = 0 + -1 -1y = 0 + -1 Combine like terms: 0 + -1 = -1 -1y = -1 Divide each side by '-1'. y = 1 Simplifying y = 1

Subproblem 4

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 5

Set the factor '(3 + -1y)' equal to zero and attempt to solve: Simplifying 3 + -1y = 0 Solving 3 + -1y = 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 + -1y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1y = 0 + -3 -1y = 0 + -3 Combine like terms: 0 + -3 = -3 -1y = -3 Divide each side by '-1'. y = 3 Simplifying y = 3

Solution

y = {0, -1, 1, -3, 3}

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