25x^2+30x-30=0

Solution for 25x^2+30x-30=0 equation:

Simplifying
25x2 + 30x + -30 = 0

Reorder the terms:
-30 + 30x + 25x2 = 0

Solving
-30 + 30x + 25x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + 6x + 5x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-6 + 6x + 5x2)' equal to zero and attempt to solve:

Simplifying
-6 + 6x + 5x2 = 0

Solving
-6 + 6x + 5x2 = 0

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

Divide each side by '5'.
-1.2 + 1.2x + x2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 1.2x + 1.2 + x2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 1.2x + x2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 1.2x + x2 = 0 + 1.2
1.2x + x2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
1.2x + x2 = 1.2

The x term is 1.2x.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2x + 0.36 + x2 = 1.2 + 0.36

Reorder the terms:
0.36 + 1.2x + x2 = 1.2 + 0.36

Combine like terms: 1.2 + 0.36 = 1.56
0.36 + 1.2x + x2 = 1.56

Factor a perfect square on the left side:
(x + 0.6)(x + 0.6) = 1.56

Calculate the square root of the right side: 1.2489996

Break this problem into two subproblems by setting 
(x + 0.6) equal to 1.2489996 and -1.2489996.

Subproblem 1
x + 0.6 = 1.2489996

Simplifying
x + 0.6 = 1.2489996

Reorder the terms:
0.6 + x = 1.2489996

Solving
0.6 + x = 1.2489996

Solving for variable 'x'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + x = 1.2489996 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + x = 1.2489996 + -0.6
x = 1.2489996 + -0.6

Combine like terms: 1.2489996 + -0.6 = 0.6489996
x = 0.6489996

Simplifying
x = 0.6489996

Subproblem 2
x + 0.6 = -1.2489996

Simplifying
x + 0.6 = -1.2489996

Reorder the terms:
0.6 + x = -1.2489996

Solving
0.6 + x = -1.2489996

Solving for variable 'x'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + x = -1.2489996 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + x = -1.2489996 + -0.6
x = -1.2489996 + -0.6

Combine like terms: -1.2489996 + -0.6 = -1.8489996
x = -1.8489996

Simplifying
x = -1.8489996

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6489996, -1.8489996}
Solution
x = {0.6489996, -1.8489996}