2y^2-56y+384=0

Solution for 2y^2-56y+384=0 equation:

Simplifying
2y2 + -56y + 384 = 0

Reorder the terms:
384 + -56y + 2y2 = 0

Solving
384 + -56y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(192 + -28y + y2) = 0

Factor a trinomial.
2((12 + -1y)(16 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(12 + -1y)' equal to zero and attempt to solve:

Simplifying
12 + -1y = 0

Solving
12 + -1y = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1y = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1y = 0 + -12
-1y = 0 + -12

Combine like terms: 0 + -12 = -12
-1y = -12

Divide each side by '-1'.
y = 12

Simplifying
y = 12
Subproblem 2
Set the factor '(16 + -1y)' equal to zero and attempt to solve:

Simplifying
16 + -1y = 0

Solving
16 + -1y = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1y = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1y = 0 + -16
-1y = 0 + -16

Combine like terms: 0 + -16 = -16
-1y = -16

Divide each side by '-1'.
y = 16

Simplifying
y = 16
Solution
y = {12, 16}