-2x(2x-3)=12

Solution for -2x(2x-3)=12 equation:

Simplifying
-2x(2x + -3) = 12

Reorder the terms:
-2x(-3 + 2x) = 12
(-3 * -2x + 2x * -2x) = 12
(6x + -4x2) = 12

Solving
6x + -4x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + 6x + -4x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 6x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 3x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + 3x + -2x2)' equal to zero and attempt to solve:

Simplifying
-6 + 3x + -2x2 = 0

Solving
-6 + 3x + -2x2 = 0

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

Divide each side by '-2'.
3 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -1.5x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -1.5x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1.5x + x2 = 0 + -3
-1.5x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1.5x + x2 = -3

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = -3 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -3 + 0.5625

Combine like terms: -3 + 0.5625 = -2.4375
0.5625 + -1.5x + x2 = -2.4375

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = -2.4375

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.