y(4y+12)=352

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Solution for y(4y+12)=352 equation: 


Simplifying
y(4y + 12) = 352

Reorder the terms:
y(12 + 4y) = 352
(12 * y + 4y * y) = 352
(12y + 4y2) = 352

Solving
12y + 4y2 = 352

Solving for variable 'y'.

Reorder the terms:
-352 + 12y + 4y2 = 352 + -352

Combine like terms: 352 + -352 = 0
-352 + 12y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-88 + 3y + y2) = 0

Factor a trinomial.
4((-11 + -1y)(8 + -1y)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-11 + -1y)' equal to zero and attempt to solve:

Simplifying
-11 + -1y = 0

Solving
-11 + -1y = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1y = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1y = 0 + 11
-1y = 0 + 11

Combine like terms: 0 + 11 = 11
-1y = 11

Divide each side by '-1'.
y = -11

Simplifying
y = -11

Subproblem 2
Set the factor '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 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 + -1y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y = 0 + -8
-1y = 0 + -8

Combine like terms: 0 + -8 = -8
-1y = -8

Divide each side by '-1'.
y = 8

Simplifying
y = 8
Solution
y = {-11, 8}

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