3y^2=y^2-5y

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Solution for 3y^2=y^2-5y equation:


Simplifying
3y2 = y2 + -5y

Reorder the terms:
3y2 = -5y + y2

Solving
3y2 = -5y + y2

Solving for variable 'y'.

Reorder the terms:
5y + 3y2 + -1y2 = -5y + y2 + 5y + -1y2

Combine like terms: 3y2 + -1y2 = 2y2
5y + 2y2 = -5y + y2 + 5y + -1y2

Reorder the terms:
5y + 2y2 = -5y + 5y + y2 + -1y2

Combine like terms: -5y + 5y = 0
5y + 2y2 = 0 + y2 + -1y2
5y + 2y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
5y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(5 + 2y) = 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 '(5 + 2y)' equal to zero and attempt to solve: Simplifying 5 + 2y = 0 Solving 5 + 2y = 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 + 2y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2y = 0 + -5 2y = 0 + -5 Combine like terms: 0 + -5 = -5 2y = -5 Divide each side by '2'. y = -2.5 Simplifying y = -2.5

Solution

y = {0, -2.5}

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