3y^2=y+10

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Solution for 3y^2=y+10 equation:


Simplifying
3y2 = y + 10

Reorder the terms:
3y2 = 10 + y

Solving
3y2 = 10 + y

Solving for variable 'y'.

Reorder the terms:
-10 + -1y + 3y2 = 10 + y + -10 + -1y

Reorder the terms:
-10 + -1y + 3y2 = 10 + -10 + y + -1y

Combine like terms: 10 + -10 = 0
-10 + -1y + 3y2 = 0 + y + -1y
-10 + -1y + 3y2 = y + -1y

Combine like terms: y + -1y = 0
-10 + -1y + 3y2 = 0

Factor a trinomial.
(-5 + -3y)(2 + -1y) = 0

Subproblem 1

Set the factor '(-5 + -3y)' equal to zero and attempt to solve: Simplifying -5 + -3y = 0 Solving -5 + -3y = 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 + -3y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3y = 0 + 5 -3y = 0 + 5 Combine like terms: 0 + 5 = 5 -3y = 5 Divide each side by '-3'. y = -1.666666667 Simplifying y = -1.666666667

Subproblem 2

Set the factor '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 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 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2

Solution

y = {-1.666666667, 2}

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