0.08(y-3)0.02y=0.14y-0.05(10)

Solution for 0.08(y-3)0.02y=0.14y-0.05(10) equation:

Simplifying
0.08(y + -3) * 0.02y = 0.14y + -0.05(10)

Reorder the terms:
0.08(-3 + y) * 0.02y = 0.14y + -0.05(10)

Reorder the terms for easier multiplication:
0.08 * 0.02y(-3 + y) = 0.14y + -0.05(10)

Multiply 0.08 * 0.02
0.0016y(-3 + y) = 0.14y + -0.05(10)
(-3 * 0.0016y + y * 0.0016y) = 0.14y + -0.05(10)
(-0.0048y + 0.0016y2) = 0.14y + -0.05(10)

Multiply -0.05 * 10
-0.0048y + 0.0016y2 = 0.14y + -0.5

Reorder the terms:
-0.0048y + 0.0016y2 = -0.5 + 0.14y

Solving
-0.0048y + 0.0016y2 = -0.5 + 0.14y

Solving for variable 'y'.

Reorder the terms:
0.5 + -0.0048y + -0.14y + 0.0016y2 = -0.5 + 0.14y + 0.5 + -0.14y

Combine like terms: -0.0048y + -0.14y = -0.1448y
0.5 + -0.1448y + 0.0016y2 = -0.5 + 0.14y + 0.5 + -0.14y

Reorder the terms:
0.5 + -0.1448y + 0.0016y2 = -0.5 + 0.5 + 0.14y + -0.14y

Combine like terms: -0.5 + 0.5 = 0.0
0.5 + -0.1448y + 0.0016y2 = 0.0 + 0.14y + -0.14y
0.5 + -0.1448y + 0.0016y2 = 0.14y + -0.14y

Combine like terms: 0.14y + -0.14y = 0.00
0.5 + -0.1448y + 0.0016y2 = 0.00

Begin completing the square.  Divide all terms by
0.0016 the coefficient of the squared term: 

Divide each side by '0.0016'.
312.5 + -90.5y + y2 = 0

Move the constant term to the right:

Add '-312.5' to each side of the equation.
312.5 + -90.5y + -312.5 + y2 = 0 + -312.5

Reorder the terms:
312.5 + -312.5 + -90.5y + y2 = 0 + -312.5

Combine like terms: 312.5 + -312.5 = 0.0
0.0 + -90.5y + y2 = 0 + -312.5
-90.5y + y2 = 0 + -312.5

Combine like terms: 0 + -312.5 = -312.5
-90.5y + y2 = -312.5

The y term is -90.5y.  Take half its coefficient (-45.25).
Square it (2047.5625) and add it to both sides.

Add '2047.5625' to each side of the equation.
-90.5y + 2047.5625 + y2 = -312.5 + 2047.5625

Reorder the terms:
2047.5625 + -90.5y + y2 = -312.5 + 2047.5625

Combine like terms: -312.5 + 2047.5625 = 1735.0625
2047.5625 + -90.5y + y2 = 1735.0625

Factor a perfect square on the left side:
(y + -45.25)(y + -45.25) = 1735.0625

Calculate the square root of the right side: 41.654081433

Break this problem into two subproblems by setting 
(y + -45.25) equal to 41.654081433 and -41.654081433.

Subproblem 1
y + -45.25 = 41.654081433

Simplifying
y + -45.25 = 41.654081433

Reorder the terms:
-45.25 + y = 41.654081433

Solving
-45.25 + y = 41.654081433

Solving for variable 'y'.

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

Add '45.25' to each side of the equation.
-45.25 + 45.25 + y = 41.654081433 + 45.25

Combine like terms: -45.25 + 45.25 = 0.00
0.00 + y = 41.654081433 + 45.25
y = 41.654081433 + 45.25

Combine like terms: 41.654081433 + 45.25 = 86.904081433
y = 86.904081433

Simplifying
y = 86.904081433

Subproblem 2
y + -45.25 = -41.654081433

Simplifying
y + -45.25 = -41.654081433

Reorder the terms:
-45.25 + y = -41.654081433

Solving
-45.25 + y = -41.654081433

Solving for variable 'y'.

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

Add '45.25' to each side of the equation.
-45.25 + 45.25 + y = -41.654081433 + 45.25

Combine like terms: -45.25 + 45.25 = 0.00
0.00 + y = -41.654081433 + 45.25
y = -41.654081433 + 45.25

Combine like terms: -41.654081433 + 45.25 = 3.595918567
y = 3.595918567

Simplifying
y = 3.595918567

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {86.904081433, 3.595918567}