x(2x-1)=2x(2x)+5x-12

Solution for x(2x-1)=2x(2x)+5x-12 equation:

Simplifying
x(2x + -1) = 2x(2x) + 5x + -12

Reorder the terms:
x(-1 + 2x) = 2x(2x) + 5x + -12
(-1 * x + 2x * x) = 2x(2x) + 5x + -12
(-1x + 2x2) = 2x(2x) + 5x + -12

Remove parenthesis around (2x)
-1x + 2x2 = 2x * 2x + 5x + -12

Reorder the terms for easier multiplication:
-1x + 2x2 = 2 * 2x * x + 5x + -12

Multiply 2 * 2
-1x + 2x2 = 4x * x + 5x + -12

Multiply x * x
-1x + 2x2 = 4x2 + 5x + -12

Reorder the terms:
-1x + 2x2 = -12 + 5x + 4x2

Solving
-1x + 2x2 = -12 + 5x + 4x2

Solving for variable 'x'.

Reorder the terms:
12 + -1x + -5x + 2x2 + -4x2 = -12 + 5x + 4x2 + 12 + -5x + -4x2

Combine like terms: -1x + -5x = -6x
12 + -6x + 2x2 + -4x2 = -12 + 5x + 4x2 + 12 + -5x + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
12 + -6x + -2x2 = -12 + 5x + 4x2 + 12 + -5x + -4x2

Reorder the terms:
12 + -6x + -2x2 = -12 + 12 + 5x + -5x + 4x2 + -4x2

Combine like terms: -12 + 12 = 0
12 + -6x + -2x2 = 0 + 5x + -5x + 4x2 + -4x2
12 + -6x + -2x2 = 5x + -5x + 4x2 + -4x2

Combine like terms: 5x + -5x = 0
12 + -6x + -2x2 = 0 + 4x2 + -4x2
12 + -6x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
12 + -6x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -3x + -1x2) = 0

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

Simplifying
6 + -3x + -1x2 = 0

Solving
6 + -3x + -1x2 = 0

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

Divide each side by '-1'.
-6 + 3x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 3x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 3x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 3x + x2 = 0 + 6
3x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
3x + x2 = 6

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 = 6 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 6 + 2.25

Combine like terms: 6 + 2.25 = 8.25
2.25 + 3x + x2 = 8.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.872281323 and -2.872281323.

Subproblem 1
x + 1.5 = 2.872281323

Simplifying
x + 1.5 = 2.872281323

Reorder the terms:
1.5 + x = 2.872281323

Solving
1.5 + x = 2.872281323

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 = 2.872281323 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 2.872281323 + -1.5
x = 2.872281323 + -1.5

Combine like terms: 2.872281323 + -1.5 = 1.372281323
x = 1.372281323

Simplifying
x = 1.372281323

Subproblem 2
x + 1.5 = -2.872281323

Simplifying
x + 1.5 = -2.872281323

Reorder the terms:
1.5 + x = -2.872281323

Solving
1.5 + x = -2.872281323

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 = -2.872281323 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -2.872281323 + -1.5
x = -2.872281323 + -1.5

Combine like terms: -2.872281323 + -1.5 = -4.372281323
x = -4.372281323

Simplifying
x = -4.372281323

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.372281323, -4.372281323}
Solution
x = {1.372281323, -4.372281323}