3x-15x^2=9

Solution for 3x-15x^2=9 equation:

Simplifying
3x + -15x2 = 9

Solving
3x + -15x2 = 9

Solving for variable 'x'.

Reorder the terms:
-9 + 3x + -15x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 3x + -15x2 = 0

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

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

Simplifying
-3 + x + -5x2 = 0

Solving
-3 + x + -5x2 = 0

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

Divide each side by '-5'.
0.6 + -0.2x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -0.2x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -0.2x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -0.2x + x2 = 0 + -0.6
-0.2x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-0.2x + x2 = -0.6

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

Add '0.25' to each side of the equation.
-0.2x + 0.25 + x2 = -0.6 + 0.25

Reorder the terms:
0.25 + -0.2x + x2 = -0.6 + 0.25

Combine like terms: -0.6 + 0.25 = -0.35
0.25 + -0.2x + x2 = -0.35

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.35

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.