82y=27y(3y+1)

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Solution for 82y=27y(3y+1) equation: 


Simplifying
82y = 27y(3y + 1)

Reorder the terms:
82y = 27y(1 + 3y)
82y = (1 * 27y + 3y * 27y)
82y = (27y + 81y2)

Solving
82y = 27y + 81y2

Solving for variable 'y'.

Combine like terms: 82y + -27y = 55y
55y + -81y2 = 27y + 81y2 + -27y + -81y2

Reorder the terms:
55y + -81y2 = 27y + -27y + 81y2 + -81y2

Combine like terms: 27y + -27y = 0
55y + -81y2 = 0 + 81y2 + -81y2
55y + -81y2 = 81y2 + -81y2

Combine like terms: 81y2 + -81y2 = 0
55y + -81y2 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(55 + -81y) = 0


Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

Move all terms containing y to the left, all other terms to the right.

Simplifying
y = 0

Subproblem 2
Set the factor '(55 + -81y)' equal to zero and attempt to solve:

Simplifying
55 + -81y = 0

Solving
55 + -81y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-55' to each side of the equation.
55 + -55 + -81y = 0 + -55

Combine like terms: 55 + -55 = 0
0 + -81y = 0 + -55
-81y = 0 + -55

Combine like terms: 0 + -55 = -55
-81y = -55

Divide each side by '-81'.
y = 0.6790123457

Simplifying
y = 0.6790123457
Solution
y = {0, 0.6790123457}

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