6y^2-11y=7

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Solution for 6y^2-11y=7 equation:


Simplifying
6y2 + -11y = 7

Reorder the terms:
-11y + 6y2 = 7

Solving
-11y + 6y2 = 7

Solving for variable 'y'.

Reorder the terms:
-7 + -11y + 6y2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -11y + 6y2 = 0

Factor a trinomial.
(-1 + -2y)(7 + -3y) = 0

Subproblem 1

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 2

Set the factor '(7 + -3y)' equal to zero and attempt to solve: Simplifying 7 + -3y = 0 Solving 7 + -3y = 0 Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3y = 0 + -7 -3y = 0 + -7 Combine like terms: 0 + -7 = -7 -3y = -7 Divide each side by '-3'. y = 2.333333333 Simplifying y = 2.333333333

Solution

y = {-0.5, 2.333333333}

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