2y^4+3y^2=7y^3

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Solution for 2y^4+3y^2=7y^3 equation:


Simplifying
2y4 + 3y2 = 7y3

Reorder the terms:
3y2 + 2y4 = 7y3

Solving
3y2 + 2y4 = 7y3

Solving for variable 'y'.

Reorder the terms:
3y2 + -7y3 + 2y4 = 7y3 + -7y3

Combine like terms: 7y3 + -7y3 = 0
3y2 + -7y3 + 2y4 = 0

Factor out the Greatest Common Factor (GCF), 'y2'.
y2(3 + -7y + 2y2) = 0

Factor a trinomial.
y2((1 + -2y)(3 + -1y)) = 0

Subproblem 1

Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y2 = 0 Take the square root of each side: y = {0}

Subproblem 2

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

Subproblem 3

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, 0.5, 3}

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