3x(2x-1)=-75

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Solution for 3x(2x-1)=-75 equation: 


Simplifying
3x(2x + -1) = -75

Reorder the terms:
3x(-1 + 2x) = -75
(-1 * 3x + 2x * 3x) = -75
(-3x + 6x2) = -75

Solving
-3x + 6x2 = -75

Solving for variable 'x'.

Reorder the terms:
75 + -3x + 6x2 = -75 + 75

Combine like terms: -75 + 75 = 0
75 + -3x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(25 + -1x + 2x2) = 0

Ignore the factor 3.

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

Simplifying
25 + -1x + 2x2 = 0

Solving
25 + -1x + 2x2 = 0

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

Divide each side by '2'.
12.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '-12.5' to each side of the equation.
12.5 + -0.5x + -12.5 + x2 = 0 + -12.5

Reorder the terms:
12.5 + -12.5 + -0.5x + x2 = 0 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + -0.5x + x2 = 0 + -12.5
-0.5x + x2 = 0 + -12.5

Combine like terms: 0 + -12.5 = -12.5
-0.5x + x2 = -12.5

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = -12.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = -12.5 + 0.0625

Combine like terms: -12.5 + 0.0625 = -12.4375
0.0625 + -0.5x + x2 = -12.4375

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = -12.4375

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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