4(2y-4)=7y(y+5)

Solution for 4(2y-4)=7y(y+5) equation:

Simplifying
4(2y + -4) = 7y(y + 5)

Reorder the terms:
4(-4 + 2y) = 7y(y + 5)
(-4 * 4 + 2y * 4) = 7y(y + 5)
(-16 + 8y) = 7y(y + 5)

Reorder the terms:
-16 + 8y = 7y(5 + y)
-16 + 8y = (5 * 7y + y * 7y)
-16 + 8y = (35y + 7y2)

Solving
-16 + 8y = 35y + 7y2

Solving for variable 'y'.

Combine like terms: 8y + -35y = -27y
-16 + -27y + -7y2 = 35y + 7y2 + -35y + -7y2

Reorder the terms:
-16 + -27y + -7y2 = 35y + -35y + 7y2 + -7y2

Combine like terms: 35y + -35y = 0
-16 + -27y + -7y2 = 0 + 7y2 + -7y2
-16 + -27y + -7y2 = 7y2 + -7y2

Combine like terms: 7y2 + -7y2 = 0
-16 + -27y + -7y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(16 + 27y + 7y2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(16 + 27y + 7y2)' equal to zero and attempt to solve:

Simplifying
16 + 27y + 7y2 = 0

Solving
16 + 27y + 7y2 = 0

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

Divide each side by '7'.
2.285714286 + 3.857142857y + y2 = 0

Move the constant term to the right:

Add '-2.285714286' to each side of the equation.
2.285714286 + 3.857142857y + -2.285714286 + y2 = 0 + -2.285714286

Reorder the terms:
2.285714286 + -2.285714286 + 3.857142857y + y2 = 0 + -2.285714286

Combine like terms: 2.285714286 + -2.285714286 = 0.000000000
0.000000000 + 3.857142857y + y2 = 0 + -2.285714286
3.857142857y + y2 = 0 + -2.285714286

Combine like terms: 0 + -2.285714286 = -2.285714286
3.857142857y + y2 = -2.285714286

The y term is 3.857142857y.  Take half its coefficient (1.928571429).
Square it (3.719387757) and add it to both sides.

Add '3.719387757' to each side of the equation.
3.857142857y + 3.719387757 + y2 = -2.285714286 + 3.719387757

Reorder the terms:
3.719387757 + 3.857142857y + y2 = -2.285714286 + 3.719387757

Combine like terms: -2.285714286 + 3.719387757 = 1.433673471
3.719387757 + 3.857142857y + y2 = 1.433673471

Factor a perfect square on the left side:
(y + 1.928571429)(y + 1.928571429) = 1.433673471

Calculate the square root of the right side: 1.197361045

Break this problem into two subproblems by setting 
(y + 1.928571429) equal to 1.197361045 and -1.197361045.

Subproblem 1
y + 1.928571429 = 1.197361045

Simplifying
y + 1.928571429 = 1.197361045

Reorder the terms:
1.928571429 + y = 1.197361045

Solving
1.928571429 + y = 1.197361045

Solving for variable 'y'.

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

Add '-1.928571429' to each side of the equation.
1.928571429 + -1.928571429 + y = 1.197361045 + -1.928571429

Combine like terms: 1.928571429 + -1.928571429 = 0.000000000
0.000000000 + y = 1.197361045 + -1.928571429
y = 1.197361045 + -1.928571429

Combine like terms: 1.197361045 + -1.928571429 = -0.731210384
y = -0.731210384

Simplifying
y = -0.731210384

Subproblem 2
y + 1.928571429 = -1.197361045

Simplifying
y + 1.928571429 = -1.197361045

Reorder the terms:
1.928571429 + y = -1.197361045

Solving
1.928571429 + y = -1.197361045

Solving for variable 'y'.

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

Add '-1.928571429' to each side of the equation.
1.928571429 + -1.928571429 + y = -1.197361045 + -1.928571429

Combine like terms: 1.928571429 + -1.928571429 = 0.000000000
0.000000000 + y = -1.197361045 + -1.928571429
y = -1.197361045 + -1.928571429

Combine like terms: -1.197361045 + -1.928571429 = -3.125932474
y = -3.125932474

Simplifying
y = -3.125932474

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.731210384, -3.125932474}
Solution
y = {-0.731210384, -3.125932474}