10y^2-30y=2

Solution for 10y^2-30y=2 equation:

Simplifying
10y2 + -30y = 2

Reorder the terms:
-30y + 10y2 = 2

Solving
-30y + 10y2 = 2

Solving for variable 'y'.

Reorder the terms:
-2 + -30y + 10y2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -30y + 10y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -15y + 5y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -15y + 5y2)' equal to zero and attempt to solve:

Simplifying
-1 + -15y + 5y2 = 0

Solving
-1 + -15y + 5y2 = 0

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

Divide each side by '5'.
-0.2 + -3y + y2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -3y + 0.2 + y2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -3y + y2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -3y + y2 = 0 + 0.2
-3y + y2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-3y + y2 = 0.2

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = 0.2 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 0.2 + 2.25

Combine like terms: 0.2 + 2.25 = 2.45
2.25 + -3y + y2 = 2.45

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 2.45

Calculate the square root of the right side: 1.565247584

Break this problem into two subproblems by setting 
(y + -1.5) equal to 1.565247584 and -1.565247584.

Subproblem 1
y + -1.5 = 1.565247584

Simplifying
y + -1.5 = 1.565247584

Reorder the terms:
-1.5 + y = 1.565247584

Solving
-1.5 + y = 1.565247584

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = 1.565247584 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 1.565247584 + 1.5
y = 1.565247584 + 1.5

Combine like terms: 1.565247584 + 1.5 = 3.065247584
y = 3.065247584

Simplifying
y = 3.065247584

Subproblem 2
y + -1.5 = -1.565247584

Simplifying
y + -1.5 = -1.565247584

Reorder the terms:
-1.5 + y = -1.565247584

Solving
-1.5 + y = -1.565247584

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = -1.565247584 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -1.565247584 + 1.5
y = -1.565247584 + 1.5

Combine like terms: -1.565247584 + 1.5 = -0.065247584
y = -0.065247584

Simplifying
y = -0.065247584

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.065247584, -0.065247584}
Solution
y = {3.065247584, -0.065247584}