3x(4-2x)=21

Solution for 3x(4-2x)=21 equation:

Simplifying
3x(4 + -2x) = 21
(4 * 3x + -2x * 3x) = 21
(12x + -6x2) = 21

Solving
12x + -6x2 = 21

Solving for variable 'x'.

Reorder the terms:
-21 + 12x + -6x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + 12x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 4x + -2x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + 4x + -2x2)' equal to zero and attempt to solve:

Simplifying
-7 + 4x + -2x2 = 0

Solving
-7 + 4x + -2x2 = 0

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

Divide each side by '-2'.
3.5 + -2x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -2x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -2x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -2x + x2 = 0 + -3.5
-2x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-2x + x2 = -3.5

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -3.5 + 1

Reorder the terms:
1 + -2x + x2 = -3.5 + 1

Combine like terms: -3.5 + 1 = -2.5
1 + -2x + x2 = -2.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = -2.5

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.