4y(y+7)=72

Solution for 4y(y+7)=72 equation:

Simplifying
4y(y + 7) = 72

Reorder the terms:
4y(7 + y) = 72
(7 * 4y + y * 4y) = 72
(28y + 4y2) = 72

Solving
28y + 4y2 = 72

Solving for variable 'y'.

Reorder the terms:
-72 + 28y + 4y2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 28y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + 7y + y2) = 0

Factor a trinomial.
4((-9 + -1y)(2 + -1y)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-9 + -1y)' equal to zero and attempt to solve:

Simplifying
-9 + -1y = 0

Solving
-9 + -1y = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1y = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1y = 0 + 9
-1y = 0 + 9

Combine like terms: 0 + 9 = 9
-1y = 9

Divide each side by '-1'.
y = -9

Simplifying
y = -9
Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-9, 2}