2y(3+y)=56

Solution for 2y(3+y)=56 equation:

Simplifying
2y(3 + y) = 56
(3 * 2y + y * 2y) = 56
(6y + 2y2) = 56

Solving
6y + 2y2 = 56

Solving for variable 'y'.

Reorder the terms:
-56 + 6y + 2y2 = 56 + -56

Combine like terms: 56 + -56 = 0
-56 + 6y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + 3y + y2) = 0

Factor a trinomial.
2((-7 + -1y)(4 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {-7, 4}