75x^2-6x+12=0

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Solution for 75x^2-6x+12=0 equation: 


Simplifying
75x2 + -6x + 12 = 0

Reorder the terms:
12 + -6x + 75x2 = 0

Solving
12 + -6x + 75x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -2x + 25x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(4 + -2x + 25x2)' equal to zero and attempt to solve:

Simplifying
4 + -2x + 25x2 = 0

Solving
4 + -2x + 25x2 = 0

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

Divide each side by '25'.
0.16 + -0.08x + x2 = 0

Move the constant term to the right:

Add '-0.16' to each side of the equation.
0.16 + -0.08x + -0.16 + x2 = 0 + -0.16

Reorder the terms:
0.16 + -0.16 + -0.08x + x2 = 0 + -0.16

Combine like terms: 0.16 + -0.16 = 0.00
0.00 + -0.08x + x2 = 0 + -0.16
-0.08x + x2 = 0 + -0.16

Combine like terms: 0 + -0.16 = -0.16
-0.08x + x2 = -0.16

The x term is -0.08x.  Take half its coefficient (-0.04).
Square it (0.0016) and add it to both sides.

Add '0.0016' to each side of the equation.
-0.08x + 0.0016 + x2 = -0.16 + 0.0016

Reorder the terms:
0.0016 + -0.08x + x2 = -0.16 + 0.0016

Combine like terms: -0.16 + 0.0016 = -0.1584
0.0016 + -0.08x + x2 = -0.1584

Factor a perfect square on the left side:
(x + -0.04)(x + -0.04) = -0.1584

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.

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