3y^2=-11y+20

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Solution for 3y^2=-11y+20 equation:


Simplifying
3y2 = -11y + 20

Reorder the terms:
3y2 = 20 + -11y

Solving
3y2 = 20 + -11y

Solving for variable 'y'.

Reorder the terms:
-20 + 11y + 3y2 = 20 + -11y + -20 + 11y

Reorder the terms:
-20 + 11y + 3y2 = 20 + -20 + -11y + 11y

Combine like terms: 20 + -20 = 0
-20 + 11y + 3y2 = 0 + -11y + 11y
-20 + 11y + 3y2 = -11y + 11y

Combine like terms: -11y + 11y = 0
-20 + 11y + 3y2 = 0

Factor a trinomial.
(-5 + -1y)(4 + -3y) = 0

Subproblem 1

Set the factor '(-5 + -1y)' equal to zero and attempt to solve: Simplifying -5 + -1y = 0 Solving -5 + -1y = 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 + -1y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1y = 0 + 5 -1y = 0 + 5 Combine like terms: 0 + 5 = 5 -1y = 5 Divide each side by '-1'. y = -5 Simplifying y = -5

Subproblem 2

Set the factor '(4 + -3y)' equal to zero and attempt to solve: Simplifying 4 + -3y = 0 Solving 4 + -3y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3y = 0 + -4 -3y = 0 + -4 Combine like terms: 0 + -4 = -4 -3y = -4 Divide each side by '-3'. y = 1.333333333 Simplifying y = 1.333333333

Solution

y = {-5, 1.333333333}

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