=3y(2y+1)+2y(y+6)

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Solution for =3y(2y+1)+2y(y+6) equation: 


Simplifying
0 = 3y(2y + 1) + 2y(y + 6)

Reorder the terms:
0 = 3y(1 + 2y) + 2y(y + 6)
0 = (1 * 3y + 2y * 3y) + 2y(y + 6)
0 = (3y + 6y2) + 2y(y + 6)

Reorder the terms:
0 = 3y + 6y2 + 2y(6 + y)
0 = 3y + 6y2 + (6 * 2y + y * 2y)
0 = 3y + 6y2 + (12y + 2y2)

Reorder the terms:
0 = 3y + 12y + 6y2 + 2y2

Combine like terms: 3y + 12y = 15y
0 = 15y + 6y2 + 2y2

Combine like terms: 6y2 + 2y2 = 8y2
0 = 15y + 8y2

Solving
0 = 15y + 8y2

Solving for variable 'y'.
Remove the zero:
-15y + -8y2 = 15y + 8y2 + -15y + -8y2

Reorder the terms:
-15y + -8y2 = 15y + -15y + 8y2 + -8y2

Combine like terms: 15y + -15y = 0
-15y + -8y2 = 0 + 8y2 + -8y2
-15y + -8y2 = 8y2 + -8y2

Combine like terms: 8y2 + -8y2 = 0
-15y + -8y2 = 0

Factor out the Greatest Common Factor (GCF), '-1y'.
-1y(15 + 8y) = 0

Ignore the factor -1.

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 '(15 + 8y)' equal to zero and attempt to solve:

Simplifying
15 + 8y = 0

Solving
15 + 8y = 0

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

Add '-15' to each side of the equation.
15 + -15 + 8y = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 8y = 0 + -15
8y = 0 + -15

Combine like terms: 0 + -15 = -15
8y = -15

Divide each side by '8'.
y = -1.875

Simplifying
y = -1.875
Solution
y = {0, -1.875}

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