7.25(7.29+-.75y)5.50y=52.75

Solution for 7.25(7.29+-.75y)5.50y=52.75 equation:

Simplifying
7.25(7.29 + -0.75y) * 5.50y = 52.75

Reorder the terms for easier multiplication:
7.25 * 5.50y(7.29 + -0.75y) = 52.75

Multiply 7.25 * 5.50
39.875y(7.29 + -0.75y) = 52.75
(7.29 * 39.875y + -0.75y * 39.875y) = 52.75
(290.68875y + -29.90625y2) = 52.75

Solving
290.68875y + -29.90625y2 = 52.75

Solving for variable 'y'.

Reorder the terms:
-52.75 + 290.68875y + -29.90625y2 = 52.75 + -52.75

Combine like terms: 52.75 + -52.75 = 0.00
-52.75 + 290.68875y + -29.90625y2 = 0.00

Begin completing the square.  Divide all terms by
-29.90625 the coefficient of the squared term: 

Divide each side by '-29.90625'.
1.76384535 + -9.72y + y2 = 0

Move the constant term to the right:

Add '-1.76384535' to each side of the equation.
1.76384535 + -9.72y + -1.76384535 + y2 = 0 + -1.76384535

Reorder the terms:
1.76384535 + -1.76384535 + -9.72y + y2 = 0 + -1.76384535

Combine like terms: 1.76384535 + -1.76384535 = 0.00000000
0.00000000 + -9.72y + y2 = 0 + -1.76384535
-9.72y + y2 = 0 + -1.76384535

Combine like terms: 0 + -1.76384535 = -1.76384535
-9.72y + y2 = -1.76384535

The y term is -9.72y.  Take half its coefficient (-4.86).
Square it (23.6196) and add it to both sides.

Add '23.6196' to each side of the equation.
-9.72y + 23.6196 + y2 = -1.76384535 + 23.6196

Reorder the terms:
23.6196 + -9.72y + y2 = -1.76384535 + 23.6196

Combine like terms: -1.76384535 + 23.6196 = 21.85575465
23.6196 + -9.72y + y2 = 21.85575465

Factor a perfect square on the left side:
(y + -4.86)(y + -4.86) = 21.85575465

Calculate the square root of the right side: 4.675013866

Break this problem into two subproblems by setting 
(y + -4.86) equal to 4.675013866 and -4.675013866.

Subproblem 1
y + -4.86 = 4.675013866

Simplifying
y + -4.86 = 4.675013866

Reorder the terms:
-4.86 + y = 4.675013866

Solving
-4.86 + y = 4.675013866

Solving for variable 'y'.

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

Add '4.86' to each side of the equation.
-4.86 + 4.86 + y = 4.675013866 + 4.86

Combine like terms: -4.86 + 4.86 = 0.00
0.00 + y = 4.675013866 + 4.86
y = 4.675013866 + 4.86

Combine like terms: 4.675013866 + 4.86 = 9.535013866
y = 9.535013866

Simplifying
y = 9.535013866

Subproblem 2
y + -4.86 = -4.675013866

Simplifying
y + -4.86 = -4.675013866

Reorder the terms:
-4.86 + y = -4.675013866

Solving
-4.86 + y = -4.675013866

Solving for variable 'y'.

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

Add '4.86' to each side of the equation.
-4.86 + 4.86 + y = -4.675013866 + 4.86

Combine like terms: -4.86 + 4.86 = 0.00
0.00 + y = -4.675013866 + 4.86
y = -4.675013866 + 4.86

Combine like terms: -4.675013866 + 4.86 = 0.184986134
y = 0.184986134

Simplifying
y = 0.184986134

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {9.535013866, 0.184986134}