5+6Y(Y+2)=5Y+8

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Solution for 5+6Y(Y+2)=5Y+8 equation: 


Simplifying
5 + 6Y(Y + 2) = 5Y + 8

Reorder the terms:
5 + 6Y(2 + Y) = 5Y + 8
5 + (2 * 6Y + Y * 6Y) = 5Y + 8
5 + (12Y + 6Y2) = 5Y + 8

Reorder the terms:
5 + 12Y + 6Y2 = 8 + 5Y

Solving
5 + 12Y + 6Y2 = 8 + 5Y

Solving for variable 'Y'.

Reorder the terms:
5 + -8 + 12Y + -5Y + 6Y2 = 8 + 5Y + -8 + -5Y

Combine like terms: 5 + -8 = -3
-3 + 12Y + -5Y + 6Y2 = 8 + 5Y + -8 + -5Y

Combine like terms: 12Y + -5Y = 7Y
-3 + 7Y + 6Y2 = 8 + 5Y + -8 + -5Y

Reorder the terms:
-3 + 7Y + 6Y2 = 8 + -8 + 5Y + -5Y

Combine like terms: 8 + -8 = 0
-3 + 7Y + 6Y2 = 0 + 5Y + -5Y
-3 + 7Y + 6Y2 = 5Y + -5Y

Combine like terms: 5Y + -5Y = 0
-3 + 7Y + 6Y2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(1 + -3Y)' equal to zero and attempt to solve:

Simplifying
1 + -3Y = 0

Solving
1 + -3Y = 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 + -3Y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3Y = 0 + -1
-3Y = 0 + -1

Combine like terms: 0 + -1 = -1
-3Y = -1

Divide each side by '-3'.
Y = 0.3333333333

Simplifying
Y = 0.3333333333
Solution
Y = {-1.5, 0.3333333333}

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