6y^2=17y-12

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Solution for 6y^2=17y-12 equation:


Simplifying
6y2 = 17y + -12

Reorder the terms:
6y2 = -12 + 17y

Solving
6y2 = -12 + 17y

Solving for variable 'y'.

Reorder the terms:
12 + -17y + 6y2 = -12 + 17y + 12 + -17y

Reorder the terms:
12 + -17y + 6y2 = -12 + 12 + 17y + -17y

Combine like terms: -12 + 12 = 0
12 + -17y + 6y2 = 0 + 17y + -17y
12 + -17y + 6y2 = 17y + -17y

Combine like terms: 17y + -17y = 0
12 + -17y + 6y2 = 0

Factor a trinomial.
(4 + -3y)(3 + -2y) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(3 + -2y)' equal to zero and attempt to solve: Simplifying 3 + -2y = 0 Solving 3 + -2y = 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 + -2y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2y = 0 + -3 -2y = 0 + -3 Combine like terms: 0 + -3 = -3 -2y = -3 Divide each side by '-2'. y = 1.5 Simplifying y = 1.5

Solution

y = {1.333333333, 1.5}

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