12x(x-3)=10

Solution for 12x(x-3)=10 equation:

Simplifying
12x(x + -3) = 10

Reorder the terms:
12x(-3 + x) = 10
(-3 * 12x + x * 12x) = 10
(-36x + 12x2) = 10

Solving
-36x + 12x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + -36x + 12x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -36x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -18x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -18x + 6x2)' equal to zero and attempt to solve:

Simplifying
-5 + -18x + 6x2 = 0

Solving
-5 + -18x + 6x2 = 0

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

Divide each side by '6'.
-0.8333333333 + -3x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -3x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -3x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -3x + x2 = 0 + 0.8333333333
-3x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-3x + x2 = 0.8333333333

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 = 0.8333333333 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 0.8333333333 + 2.25

Combine like terms: 0.8333333333 + 2.25 = 3.0833333333
2.25 + -3x + x2 = 3.0833333333

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 3.0833333333

Calculate the square root of the right side: 1.755942292

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.755942292 and -1.755942292.

Subproblem 1
x + -1.5 = 1.755942292

Simplifying
x + -1.5 = 1.755942292

Reorder the terms:
-1.5 + x = 1.755942292

Solving
-1.5 + x = 1.755942292

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 1.755942292 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 1.755942292 + 1.5
x = 1.755942292 + 1.5

Combine like terms: 1.755942292 + 1.5 = 3.255942292
x = 3.255942292

Simplifying
x = 3.255942292

Subproblem 2
x + -1.5 = -1.755942292

Simplifying
x + -1.5 = -1.755942292

Reorder the terms:
-1.5 + x = -1.755942292

Solving
-1.5 + x = -1.755942292

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -1.755942292 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -1.755942292 + 1.5
x = -1.755942292 + 1.5

Combine like terms: -1.755942292 + 1.5 = -0.255942292
x = -0.255942292

Simplifying
x = -0.255942292

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.255942292, -0.255942292}
Solution
x = {3.255942292, -0.255942292}