4y(y-7)=2y-38

Solution for 4y(y-7)=2y-38 equation:

Simplifying
4y(y + -7) = 2y + -38

Reorder the terms:
4y(-7 + y) = 2y + -38
(-7 * 4y + y * 4y) = 2y + -38
(-28y + 4y2) = 2y + -38

Reorder the terms:
-28y + 4y2 = -38 + 2y

Solving
-28y + 4y2 = -38 + 2y

Solving for variable 'y'.

Reorder the terms:
38 + -28y + -2y + 4y2 = -38 + 2y + 38 + -2y

Combine like terms: -28y + -2y = -30y
38 + -30y + 4y2 = -38 + 2y + 38 + -2y

Reorder the terms:
38 + -30y + 4y2 = -38 + 38 + 2y + -2y

Combine like terms: -38 + 38 = 0
38 + -30y + 4y2 = 0 + 2y + -2y
38 + -30y + 4y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
38 + -30y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(19 + -15y + 2y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(19 + -15y + 2y2)' equal to zero and attempt to solve:

Simplifying
19 + -15y + 2y2 = 0

Solving
19 + -15y + 2y2 = 0

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

Divide each side by '2'.
9.5 + -7.5y + y2 = 0

Move the constant term to the right:

Add '-9.5' to each side of the equation.
9.5 + -7.5y + -9.5 + y2 = 0 + -9.5

Reorder the terms:
9.5 + -9.5 + -7.5y + y2 = 0 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + -7.5y + y2 = 0 + -9.5
-7.5y + y2 = 0 + -9.5

Combine like terms: 0 + -9.5 = -9.5
-7.5y + y2 = -9.5

The y term is -7.5y.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5y + 14.0625 + y2 = -9.5 + 14.0625

Reorder the terms:
14.0625 + -7.5y + y2 = -9.5 + 14.0625

Combine like terms: -9.5 + 14.0625 = 4.5625
14.0625 + -7.5y + y2 = 4.5625

Factor a perfect square on the left side:
(y + -3.75)(y + -3.75) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(y + -3.75) equal to 2.136000936 and -2.136000936.

Subproblem 1
y + -3.75 = 2.136000936

Simplifying
y + -3.75 = 2.136000936

Reorder the terms:
-3.75 + y = 2.136000936

Solving
-3.75 + y = 2.136000936

Solving for variable 'y'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + y = 2.136000936 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + y = 2.136000936 + 3.75
y = 2.136000936 + 3.75

Combine like terms: 2.136000936 + 3.75 = 5.886000936
y = 5.886000936

Simplifying
y = 5.886000936

Subproblem 2
y + -3.75 = -2.136000936

Simplifying
y + -3.75 = -2.136000936

Reorder the terms:
-3.75 + y = -2.136000936

Solving
-3.75 + y = -2.136000936

Solving for variable 'y'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + y = -2.136000936 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + y = -2.136000936 + 3.75
y = -2.136000936 + 3.75

Combine like terms: -2.136000936 + 3.75 = 1.613999064
y = 1.613999064

Simplifying
y = 1.613999064

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.886000936, 1.613999064}
Solution
y = {5.886000936, 1.613999064}