6-3(5x^2-3x+5)=0

Solution for 6-3(5x^2-3x+5)=0 equation:

Simplifying
6 + -3(5x2 + -3x + 5) = 0

Reorder the terms:
6 + -3(5 + -3x + 5x2) = 0
6 + (5 * -3 + -3x * -3 + 5x2 * -3) = 0
6 + (-15 + 9x + -15x2) = 0

Combine like terms: 6 + -15 = -9
-9 + 9x + -15x2 = 0

Solving
-9 + 9x + -15x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-3 + 3x + -5x2 = 0

Solving
-3 + 3x + -5x2 = 0

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

Divide each side by '-5'.
0.6 + -0.6x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -0.6x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -0.6x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -0.6x + x2 = 0 + -0.6
-0.6x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-0.6x + x2 = -0.6

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = -0.6 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = -0.6 + 0.09

Combine like terms: -0.6 + 0.09 = -0.51
0.09 + -0.6x + x2 = -0.51

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = -0.51

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.