y=-3y^2+6y+8

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Solution for y=-3y^2+6y+8 equation: 


Simplifying
y = -3y2 + 6y + 8

Reorder the terms:
y = 8 + 6y + -3y2

Solving
y = 8 + 6y + -3y2

Solving for variable 'y'.

Reorder the terms:
-8 + y + -6y + 3y2 = 8 + 6y + -3y2 + -8 + -6y + 3y2

Combine like terms: y + -6y = -5y
-8 + -5y + 3y2 = 8 + 6y + -3y2 + -8 + -6y + 3y2

Reorder the terms:
-8 + -5y + 3y2 = 8 + -8 + 6y + -6y + -3y2 + 3y2

Combine like terms: 8 + -8 = 0
-8 + -5y + 3y2 = 0 + 6y + -6y + -3y2 + 3y2
-8 + -5y + 3y2 = 6y + -6y + -3y2 + 3y2

Combine like terms: 6y + -6y = 0
-8 + -5y + 3y2 = 0 + -3y2 + 3y2
-8 + -5y + 3y2 = -3y2 + 3y2

Combine like terms: -3y2 + 3y2 = 0
-8 + -5y + 3y2 = 0

Factor a trinomial.
(-1 + -1y)(8 + -3y) = 0


Subproblem 1
Set the factor '(-1 + -1y)' equal to zero and attempt to solve:

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 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 + -1y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1y = 0 + 1
-1y = 0 + 1

Combine like terms: 0 + 1 = 1
-1y = 1

Divide each side by '-1'.
y = -1

Simplifying
y = -1

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 = {-1, 2.666666667}

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