10x^2+48x-60=0

Solution for 10x^2+48x-60=0 equation:

Simplifying
10x2 + 48x + -60 = 0

Reorder the terms:
-60 + 48x + 10x2 = 0

Solving
-60 + 48x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + 24x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-30 + 24x + 5x2)' equal to zero and attempt to solve:

Simplifying
-30 + 24x + 5x2 = 0

Solving
-30 + 24x + 5x2 = 0

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

Divide each side by '5'.
-6 + 4.8x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 4.8x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 4.8x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 4.8x + x2 = 0 + 6
4.8x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
4.8x + x2 = 6

The x term is 4.8x.  Take half its coefficient (2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
4.8x + 5.76 + x2 = 6 + 5.76

Reorder the terms:
5.76 + 4.8x + x2 = 6 + 5.76

Combine like terms: 6 + 5.76 = 11.76
5.76 + 4.8x + x2 = 11.76

Factor a perfect square on the left side:
(x + 2.4)(x + 2.4) = 11.76

Calculate the square root of the right side: 3.42928564

Break this problem into two subproblems by setting 
(x + 2.4) equal to 3.42928564 and -3.42928564.

Subproblem 1
x + 2.4 = 3.42928564

Simplifying
x + 2.4 = 3.42928564

Reorder the terms:
2.4 + x = 3.42928564

Solving
2.4 + x = 3.42928564

Solving for variable 'x'.

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

Add '-2.4' to each side of the equation.
2.4 + -2.4 + x = 3.42928564 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + x = 3.42928564 + -2.4
x = 3.42928564 + -2.4

Combine like terms: 3.42928564 + -2.4 = 1.02928564
x = 1.02928564

Simplifying
x = 1.02928564

Subproblem 2
x + 2.4 = -3.42928564

Simplifying
x + 2.4 = -3.42928564

Reorder the terms:
2.4 + x = -3.42928564

Solving
2.4 + x = -3.42928564

Solving for variable 'x'.

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

Add '-2.4' to each side of the equation.
2.4 + -2.4 + x = -3.42928564 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + x = -3.42928564 + -2.4
x = -3.42928564 + -2.4

Combine like terms: -3.42928564 + -2.4 = -5.82928564
x = -5.82928564

Simplifying
x = -5.82928564

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.02928564, -5.82928564}
Solution
x = {1.02928564, -5.82928564}