30x^2+15x-6=0

Solution for 30x^2+15x-6=0 equation:

Simplifying
30x2 + 15x + -6 = 0

Reorder the terms:
-6 + 15x + 30x2 = 0

Solving
-6 + 15x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 5x + 10x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + 5x + 10x2)' equal to zero and attempt to solve:

Simplifying
-2 + 5x + 10x2 = 0

Solving
-2 + 5x + 10x2 = 0

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

Divide each side by '10'.
-0.2 + 0.5x + x2 = 0.0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 0.5x + 0.2 + x2 = 0.0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 0.5x + x2 = 0.0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 0.5x + x2 = 0.0 + 0.2
0.5x + x2 = 0.0 + 0.2

Combine like terms: 0.0 + 0.2 = 0.2
0.5x + x2 = 0.2

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 0.2 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 0.2 + 0.0625

Combine like terms: 0.2 + 0.0625 = 0.2625
0.0625 + 0.5x + x2 = 0.2625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 0.2625

Calculate the square root of the right side: 0.512347538

Break this problem into two subproblems by setting 
(x + 0.25) equal to 0.512347538 and -0.512347538.

Subproblem 1
x + 0.25 = 0.512347538

Simplifying
x + 0.25 = 0.512347538

Reorder the terms:
0.25 + x = 0.512347538

Solving
0.25 + x = 0.512347538

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 0.512347538 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 0.512347538 + -0.25
x = 0.512347538 + -0.25

Combine like terms: 0.512347538 + -0.25 = 0.262347538
x = 0.262347538

Simplifying
x = 0.262347538

Subproblem 2
x + 0.25 = -0.512347538

Simplifying
x + 0.25 = -0.512347538

Reorder the terms:
0.25 + x = -0.512347538

Solving
0.25 + x = -0.512347538

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -0.512347538 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -0.512347538 + -0.25
x = -0.512347538 + -0.25

Combine like terms: -0.512347538 + -0.25 = -0.762347538
x = -0.762347538

Simplifying
x = -0.762347538

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.262347538, -0.762347538}
Solution
x = {0.262347538, -0.762347538}