3(y-5)y=7

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Solution for 3(y-5)y=7 equation: 


Simplifying
3(y + -5) * y = 7

Reorder the terms:
3(-5 + y) * y = 7

Reorder the terms for easier multiplication:
3y(-5 + y) = 7
(-5 * 3y + y * 3y) = 7
(-15y + 3y2) = 7

Solving
-15y + 3y2 = 7

Solving for variable 'y'.

Reorder the terms:
-7 + -15y + 3y2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -15y + 3y2 = 0

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

Divide each side by '3'.
-2.333333333 + -5y + y2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -5y + 2.333333333 + y2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -5y + y2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -5y + y2 = 0 + 2.333333333
-5y + y2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-5y + y2 = 2.333333333

The y term is -5y.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5y + 6.25 + y2 = 2.333333333 + 6.25

Reorder the terms:
6.25 + -5y + y2 = 2.333333333 + 6.25

Combine like terms: 2.333333333 + 6.25 = 8.583333333
6.25 + -5y + y2 = 8.583333333

Factor a perfect square on the left side:
(y + -2.5)(y + -2.5) = 8.583333333

Calculate the square root of the right side: 2.929732638

Break this problem into two subproblems by setting 
(y + -2.5) equal to 2.929732638 and -2.929732638.


Subproblem 1
y + -2.5 = 2.929732638

Simplifying
y + -2.5 = 2.929732638

Reorder the terms:
-2.5 + y = 2.929732638

Solving
-2.5 + y = 2.929732638

Solving for variable 'y'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + y = 2.929732638 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = 2.929732638 + 2.5
y = 2.929732638 + 2.5

Combine like terms: 2.929732638 + 2.5 = 5.429732638
y = 5.429732638

Simplifying
y = 5.429732638


Subproblem 2
y + -2.5 = -2.929732638

Simplifying
y + -2.5 = -2.929732638

Reorder the terms:
-2.5 + y = -2.929732638

Solving
-2.5 + y = -2.929732638

Solving for variable 'y'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + y = -2.929732638 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = -2.929732638 + 2.5
y = -2.929732638 + 2.5

Combine like terms: -2.929732638 + 2.5 = -0.429732638
y = -0.429732638

Simplifying
y = -0.429732638


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.429732638, -0.429732638}

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