6y(2y-5)=30

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Solution for 6y(2y-5)=30 equation: 


Simplifying
6y(2y + -5) = 30

Reorder the terms:
6y(-5 + 2y) = 30
(-5 * 6y + 2y * 6y) = 30
(-30y + 12y2) = 30

Solving
-30y + 12y2 = 30

Solving for variable 'y'.

Reorder the terms:
-30 + -30y + 12y2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -30y + 12y2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-5 + -5y + 2y2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-5 + -5y + 2y2)' equal to zero and attempt to solve:

Simplifying
-5 + -5y + 2y2 = 0

Solving
-5 + -5y + 2y2 = 0

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

Divide each side by '2'.
-2.5 + -2.5y + y2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -2.5y + 2.5 + y2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -2.5y + y2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -2.5y + y2 = 0 + 2.5
-2.5y + y2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-2.5y + y2 = 2.5

The y term is -2.5y.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5y + 1.5625 + y2 = 2.5 + 1.5625

Reorder the terms:
1.5625 + -2.5y + y2 = 2.5 + 1.5625

Combine like terms: 2.5 + 1.5625 = 4.0625
1.5625 + -2.5y + y2 = 4.0625

Factor a perfect square on the left side:
(y + -1.25)(y + -1.25) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(y + -1.25) equal to 2.015564437 and -2.015564437.


Subproblem 1
y + -1.25 = 2.015564437

Simplifying
y + -1.25 = 2.015564437

Reorder the terms:
-1.25 + y = 2.015564437

Solving
-1.25 + y = 2.015564437

Solving for variable 'y'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + y = 2.015564437 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = 2.015564437 + 1.25
y = 2.015564437 + 1.25

Combine like terms: 2.015564437 + 1.25 = 3.265564437
y = 3.265564437

Simplifying
y = 3.265564437


Subproblem 2
y + -1.25 = -2.015564437

Simplifying
y + -1.25 = -2.015564437

Reorder the terms:
-1.25 + y = -2.015564437

Solving
-1.25 + y = -2.015564437

Solving for variable 'y'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + y = -2.015564437 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = -2.015564437 + 1.25
y = -2.015564437 + 1.25

Combine like terms: -2.015564437 + 1.25 = -0.765564437
y = -0.765564437

Simplifying
y = -0.765564437


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.265564437, -0.765564437}
Solution
y = {3.265564437, -0.765564437}

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