2y(y+4)=42

Solution for 2y(y+4)=42 equation:

Simplifying
2y(y + 4) = 42

Reorder the terms:
2y(4 + y) = 42
(4 * 2y + y * 2y) = 42
(8y + 2y2) = 42

Solving
8y + 2y2 = 42

Solving for variable 'y'.

Reorder the terms:
-42 + 8y + 2y2 = 42 + -42

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

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

Factor a trinomial.
2((-7 + -1y)(3 + -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 '(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
Solution
y = {-7, 3}