4(2y+9)7y=-24

Solution for 4(2y+9)7y=-24 equation:

Simplifying
4(2y + 9) * 7y = -24

Reorder the terms:
4(9 + 2y) * 7y = -24

Reorder the terms for easier multiplication:
4 * 7y(9 + 2y) = -24

Multiply 4 * 7
28y(9 + 2y) = -24
(9 * 28y + 2y * 28y) = -24
(252y + 56y2) = -24

Solving
252y + 56y2 = -24

Solving for variable 'y'.

Reorder the terms:
24 + 252y + 56y2 = -24 + 24

Combine like terms: -24 + 24 = 0
24 + 252y + 56y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + 63y + 14y2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(6 + 63y + 14y2)' equal to zero and attempt to solve:

Simplifying
6 + 63y + 14y2 = 0

Solving
6 + 63y + 14y2 = 0

Begin completing the square.  Divide all terms by
14 the coefficient of the squared term: 

Divide each side by '14'.
0.4285714286 + 4.5y + y2 = 0

Move the constant term to the right:

Add '-0.4285714286' to each side of the equation.
0.4285714286 + 4.5y + -0.4285714286 + y2 = 0 + -0.4285714286

Reorder the terms:
0.4285714286 + -0.4285714286 + 4.5y + y2 = 0 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + 4.5y + y2 = 0 + -0.4285714286
4.5y + y2 = 0 + -0.4285714286

Combine like terms: 0 + -0.4285714286 = -0.4285714286
4.5y + y2 = -0.4285714286

The y term is 4.5y.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5y + 5.0625 + y2 = -0.4285714286 + 5.0625

Reorder the terms:
5.0625 + 4.5y + y2 = -0.4285714286 + 5.0625

Combine like terms: -0.4285714286 + 5.0625 = 4.6339285714
5.0625 + 4.5y + y2 = 4.6339285714

Factor a perfect square on the left side:
(y + 2.25)(y + 2.25) = 4.6339285714

Calculate the square root of the right side: 2.152656167

Break this problem into two subproblems by setting 
(y + 2.25) equal to 2.152656167 and -2.152656167.

Subproblem 1
y + 2.25 = 2.152656167

Simplifying
y + 2.25 = 2.152656167

Reorder the terms:
2.25 + y = 2.152656167

Solving
2.25 + y = 2.152656167

Solving for variable 'y'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + y = 2.152656167 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + y = 2.152656167 + -2.25
y = 2.152656167 + -2.25

Combine like terms: 2.152656167 + -2.25 = -0.097343833
y = -0.097343833

Simplifying
y = -0.097343833

Subproblem 2
y + 2.25 = -2.152656167

Simplifying
y + 2.25 = -2.152656167

Reorder the terms:
2.25 + y = -2.152656167

Solving
2.25 + y = -2.152656167

Solving for variable 'y'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + y = -2.152656167 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + y = -2.152656167 + -2.25
y = -2.152656167 + -2.25

Combine like terms: -2.152656167 + -2.25 = -4.402656167
y = -4.402656167

Simplifying
y = -4.402656167

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.097343833, -4.402656167}
Solution
y = {-0.097343833, -4.402656167}