3x(6-2x)=30

Solution for 3x(6-2x)=30 equation:

Simplifying
3x(6 + -2x) = 30
(6 * 3x + -2x * 3x) = 30
(18x + -6x2) = 30

Solving
18x + -6x2 = 30

Solving for variable 'x'.

Reorder the terms:
-30 + 18x + -6x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 18x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-5 + 3x + -1x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-5 + 3x + -1x2)' equal to zero and attempt to solve:

Simplifying
-5 + 3x + -1x2 = 0

Solving
-5 + 3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
5 + -3x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -3x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -3x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x + x2 = 0 + -5
-3x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-3x + x2 = -5

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -5 + 2.25

Combine like terms: -5 + 2.25 = -2.75
2.25 + -3x + x2 = -2.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -2.75

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.