27y^2=48y+64

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Solution for 27y^2=48y+64 equation:


Simplifying
27y2 = 48y + 64

Reorder the terms:
27y2 = 64 + 48y

Solving
27y2 = 64 + 48y

Solving for variable 'y'.

Reorder the terms:
-64 + -48y + 27y2 = 64 + 48y + -64 + -48y

Reorder the terms:
-64 + -48y + 27y2 = 64 + -64 + 48y + -48y

Combine like terms: 64 + -64 = 0
-64 + -48y + 27y2 = 0 + 48y + -48y
-64 + -48y + 27y2 = 48y + -48y

Combine like terms: 48y + -48y = 0
-64 + -48y + 27y2 = 0

Factor a trinomial.
(-8 + -9y)(8 + -3y) = 0

Subproblem 1

Set the factor '(-8 + -9y)' equal to zero and attempt to solve: Simplifying -8 + -9y = 0 Solving -8 + -9y = 0 Move all terms containing y to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -9y = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -9y = 0 + 8 -9y = 0 + 8 Combine like terms: 0 + 8 = 8 -9y = 8 Divide each side by '-9'. y = -0.8888888889 Simplifying y = -0.8888888889

Subproblem 2

Set the factor '(8 + -3y)' equal to zero and attempt to solve: Simplifying 8 + -3y = 0 Solving 8 + -3y = 0 Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3y = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3y = 0 + -8 -3y = 0 + -8 Combine like terms: 0 + -8 = -8 -3y = -8 Divide each side by '-3'. y = 2.666666667 Simplifying y = 2.666666667

Solution

y = {-0.8888888889, 2.666666667}

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