312=2x(x-3)

Solution for 312=2x(x-3) equation:

Simplifying
312 = 2x(x + -3)

Reorder the terms:
312 = 2x(-3 + x)
312 = (-3 * 2x + x * 2x)
312 = (-6x + 2x2)

Solving
312 = -6x + 2x2

Solving for variable 'x'.

Reorder the terms:
312 + 6x + -2x2 = -6x + 6x + 2x2 + -2x2

Combine like terms: -6x + 6x = 0
312 + 6x + -2x2 = 0 + 2x2 + -2x2
312 + 6x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
312 + 6x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(156 + 3x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(156 + 3x + -1x2)' equal to zero and attempt to solve:

Simplifying
156 + 3x + -1x2 = 0

Solving
156 + 3x + -1x2 = 0

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

Divide each side by '-1'.
-156 + -3x + x2 = 0

Move the constant term to the right:

Add '156' to each side of the equation.
-156 + -3x + 156 + x2 = 0 + 156

Reorder the terms:
-156 + 156 + -3x + x2 = 0 + 156

Combine like terms: -156 + 156 = 0
0 + -3x + x2 = 0 + 156
-3x + x2 = 0 + 156

Combine like terms: 0 + 156 = 156
-3x + x2 = 156

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 = 156 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 156 + 2.25

Combine like terms: 156 + 2.25 = 158.25
2.25 + -3x + x2 = 158.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 158.25

Calculate the square root of the right side: 12.579745625

Break this problem into two subproblems by setting 
(x + -1.5) equal to 12.579745625 and -12.579745625.

Subproblem 1
x + -1.5 = 12.579745625

Simplifying
x + -1.5 = 12.579745625

Reorder the terms:
-1.5 + x = 12.579745625

Solving
-1.5 + x = 12.579745625

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 = 12.579745625 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 12.579745625 + 1.5
x = 12.579745625 + 1.5

Combine like terms: 12.579745625 + 1.5 = 14.079745625
x = 14.079745625

Simplifying
x = 14.079745625

Subproblem 2
x + -1.5 = -12.579745625

Simplifying
x + -1.5 = -12.579745625

Reorder the terms:
-1.5 + x = -12.579745625

Solving
-1.5 + x = -12.579745625

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 = -12.579745625 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -12.579745625 + 1.5
x = -12.579745625 + 1.5

Combine like terms: -12.579745625 + 1.5 = -11.079745625
x = -11.079745625

Simplifying
x = -11.079745625

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.079745625, -11.079745625}
Solution
x = {14.079745625, -11.079745625}