3y(y+3)+5y=8y+4+5

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Solution for 3y(y+3)+5y=8y+4+5 equation: 


Simplifying
3y(y + 3) + 5y = 8y + 4 + 5

Reorder the terms:
3y(3 + y) + 5y = 8y + 4 + 5
(3 * 3y + y * 3y) + 5y = 8y + 4 + 5
(9y + 3y2) + 5y = 8y + 4 + 5

Reorder the terms:
9y + 5y + 3y2 = 8y + 4 + 5

Combine like terms: 9y + 5y = 14y
14y + 3y2 = 8y + 4 + 5

Reorder the terms:
14y + 3y2 = 4 + 5 + 8y

Combine like terms: 4 + 5 = 9
14y + 3y2 = 9 + 8y

Solving
14y + 3y2 = 9 + 8y

Solving for variable 'y'.

Reorder the terms:
-9 + 14y + -8y + 3y2 = 9 + 8y + -9 + -8y

Combine like terms: 14y + -8y = 6y
-9 + 6y + 3y2 = 9 + 8y + -9 + -8y

Reorder the terms:
-9 + 6y + 3y2 = 9 + -9 + 8y + -8y

Combine like terms: 9 + -9 = 0
-9 + 6y + 3y2 = 0 + 8y + -8y
-9 + 6y + 3y2 = 8y + -8y

Combine like terms: 8y + -8y = 0
-9 + 6y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 2y + y2) = 0

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

Ignore the factor 3.

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

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 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 + -1y = 0 + 3

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

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

Divide each side by '-1'.
y = -3

Simplifying
y = -3

Subproblem 2
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
Solution
y = {-3, 1}

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