12(5x-1)=7x(10x-4)

Solution for 12(5x-1)=7x(10x-4) equation:

Simplifying
12(5x + -1) = 7x(10x + -4)

Reorder the terms:
12(-1 + 5x) = 7x(10x + -4)
(-1 * 12 + 5x * 12) = 7x(10x + -4)
(-12 + 60x) = 7x(10x + -4)

Reorder the terms:
-12 + 60x = 7x(-4 + 10x)
-12 + 60x = (-4 * 7x + 10x * 7x)
-12 + 60x = (-28x + 70x2)

Solving
-12 + 60x = -28x + 70x2

Solving for variable 'x'.

Combine like terms: 60x + 28x = 88x
-12 + 88x + -70x2 = -28x + 70x2 + 28x + -70x2

Reorder the terms:
-12 + 88x + -70x2 = -28x + 28x + 70x2 + -70x2

Combine like terms: -28x + 28x = 0
-12 + 88x + -70x2 = 0 + 70x2 + -70x2
-12 + 88x + -70x2 = 70x2 + -70x2

Combine like terms: 70x2 + -70x2 = 0
-12 + 88x + -70x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 44x + -35x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + 44x + -35x2)' equal to zero and attempt to solve:

Simplifying
-6 + 44x + -35x2 = 0

Solving
-6 + 44x + -35x2 = 0

Begin completing the square.  Divide all terms by
-35 the coefficient of the squared term: 

Divide each side by '-35'.
0.1714285714 + -1.257142857x + x2 = 0

Move the constant term to the right:

Add '-0.1714285714' to each side of the equation.
0.1714285714 + -1.257142857x + -0.1714285714 + x2 = 0 + -0.1714285714

Reorder the terms:
0.1714285714 + -0.1714285714 + -1.257142857x + x2 = 0 + -0.1714285714

Combine like terms: 0.1714285714 + -0.1714285714 = 0.0000000000
0.0000000000 + -1.257142857x + x2 = 0 + -0.1714285714
-1.257142857x + x2 = 0 + -0.1714285714

Combine like terms: 0 + -0.1714285714 = -0.1714285714
-1.257142857x + x2 = -0.1714285714

The x term is -1.257142857x.  Take half its coefficient (-0.6285714285).
Square it (0.3951020407) and add it to both sides.

Add '0.3951020407' to each side of the equation.
-1.257142857x + 0.3951020407 + x2 = -0.1714285714 + 0.3951020407

Reorder the terms:
0.3951020407 + -1.257142857x + x2 = -0.1714285714 + 0.3951020407

Combine like terms: -0.1714285714 + 0.3951020407 = 0.2236734693
0.3951020407 + -1.257142857x + x2 = 0.2236734693

Factor a perfect square on the left side:
(x + -0.6285714285)(x + -0.6285714285) = 0.2236734693

Calculate the square root of the right side: 0.472941296

Break this problem into two subproblems by setting 
(x + -0.6285714285) equal to 0.472941296 and -0.472941296.

Subproblem 1
x + -0.6285714285 = 0.472941296

Simplifying
x + -0.6285714285 = 0.472941296

Reorder the terms:
-0.6285714285 + x = 0.472941296

Solving
-0.6285714285 + x = 0.472941296

Solving for variable 'x'.

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

Add '0.6285714285' to each side of the equation.
-0.6285714285 + 0.6285714285 + x = 0.472941296 + 0.6285714285

Combine like terms: -0.6285714285 + 0.6285714285 = 0.0000000000
0.0000000000 + x = 0.472941296 + 0.6285714285
x = 0.472941296 + 0.6285714285

Combine like terms: 0.472941296 + 0.6285714285 = 1.1015127245
x = 1.1015127245

Simplifying
x = 1.1015127245

Subproblem 2
x + -0.6285714285 = -0.472941296

Simplifying
x + -0.6285714285 = -0.472941296

Reorder the terms:
-0.6285714285 + x = -0.472941296

Solving
-0.6285714285 + x = -0.472941296

Solving for variable 'x'.

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

Add '0.6285714285' to each side of the equation.
-0.6285714285 + 0.6285714285 + x = -0.472941296 + 0.6285714285

Combine like terms: -0.6285714285 + 0.6285714285 = 0.0000000000
0.0000000000 + x = -0.472941296 + 0.6285714285
x = -0.472941296 + 0.6285714285

Combine like terms: -0.472941296 + 0.6285714285 = 0.1556301325
x = 0.1556301325

Simplifying
x = 0.1556301325

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1015127245, 0.1556301325}
Solution
x = {1.1015127245, 0.1556301325}