y(2y+6)-4(2y+6)-3(2y+6)=0

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Solution for y(2y+6)-4(2y+6)-3(2y+6)=0 equation: 


Simplifying
y(2y + 6) + -4(2y + 6) + -3(2y + 6) = 0

Reorder the terms:
y(6 + 2y) + -4(2y + 6) + -3(2y + 6) = 0
(6 * y + 2y * y) + -4(2y + 6) + -3(2y + 6) = 0
(6y + 2y2) + -4(2y + 6) + -3(2y + 6) = 0

Reorder the terms:
6y + 2y2 + -4(6 + 2y) + -3(2y + 6) = 0
6y + 2y2 + (6 * -4 + 2y * -4) + -3(2y + 6) = 0
6y + 2y2 + (-24 + -8y) + -3(2y + 6) = 0

Reorder the terms:
6y + 2y2 + -24 + -8y + -3(6 + 2y) = 0
6y + 2y2 + -24 + -8y + (6 * -3 + 2y * -3) = 0
6y + 2y2 + -24 + -8y + (-18 + -6y) = 0

Reorder the terms:
-24 + -18 + 6y + -8y + -6y + 2y2 = 0

Combine like terms: -24 + -18 = -42
-42 + 6y + -8y + -6y + 2y2 = 0

Combine like terms: 6y + -8y = -2y
-42 + -2y + -6y + 2y2 = 0

Combine like terms: -2y + -6y = -8y
-42 + -8y + 2y2 = 0

Solving
-42 + -8y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -4y + y2) = 0

Factor a trinomial.
2((-3 + -1y)(7 + -1y)) = 0

Ignore the factor 2.

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 '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7
Solution
y = {-3, 7}

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