12(5x+1)=7x(2x+2)

Solution for 12(5x+1)=7x(2x+2) equation:

Simplifying
12(5x + 1) = 7x(2x + 2)

Reorder the terms:
12(1 + 5x) = 7x(2x + 2)
(1 * 12 + 5x * 12) = 7x(2x + 2)
(12 + 60x) = 7x(2x + 2)

Reorder the terms:
12 + 60x = 7x(2 + 2x)
12 + 60x = (2 * 7x + 2x * 7x)
12 + 60x = (14x + 14x2)

Solving
12 + 60x = 14x + 14x2

Solving for variable 'x'.

Combine like terms: 60x + -14x = 46x
12 + 46x + -14x2 = 14x + 14x2 + -14x + -14x2

Reorder the terms:
12 + 46x + -14x2 = 14x + -14x + 14x2 + -14x2

Combine like terms: 14x + -14x = 0
12 + 46x + -14x2 = 0 + 14x2 + -14x2
12 + 46x + -14x2 = 14x2 + -14x2

Combine like terms: 14x2 + -14x2 = 0
12 + 46x + -14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 23x + -7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + 23x + -7x2)' equal to zero and attempt to solve:

Simplifying
6 + 23x + -7x2 = 0

Solving
6 + 23x + -7x2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-0.8571428571 + -3.285714286x + x2 = 0

Move the constant term to the right:

Add '0.8571428571' to each side of the equation.
-0.8571428571 + -3.285714286x + 0.8571428571 + x2 = 0 + 0.8571428571

Reorder the terms:
-0.8571428571 + 0.8571428571 + -3.285714286x + x2 = 0 + 0.8571428571

Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000
0.0000000000 + -3.285714286x + x2 = 0 + 0.8571428571
-3.285714286x + x2 = 0 + 0.8571428571

Combine like terms: 0 + 0.8571428571 = 0.8571428571
-3.285714286x + x2 = 0.8571428571

The x term is -3.285714286x.  Take half its coefficient (-1.642857143).
Square it (2.698979592) and add it to both sides.

Add '2.698979592' to each side of the equation.
-3.285714286x + 2.698979592 + x2 = 0.8571428571 + 2.698979592

Reorder the terms:
2.698979592 + -3.285714286x + x2 = 0.8571428571 + 2.698979592

Combine like terms: 0.8571428571 + 2.698979592 = 3.5561224491
2.698979592 + -3.285714286x + x2 = 3.5561224491

Factor a perfect square on the left side:
(x + -1.642857143)(x + -1.642857143) = 3.5561224491

Calculate the square root of the right side: 1.885768398

Break this problem into two subproblems by setting 
(x + -1.642857143) equal to 1.885768398 and -1.885768398.

Subproblem 1
x + -1.642857143 = 1.885768398

Simplifying
x + -1.642857143 = 1.885768398

Reorder the terms:
-1.642857143 + x = 1.885768398

Solving
-1.642857143 + x = 1.885768398

Solving for variable 'x'.

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

Add '1.642857143' to each side of the equation.
-1.642857143 + 1.642857143 + x = 1.885768398 + 1.642857143

Combine like terms: -1.642857143 + 1.642857143 = 0.000000000
0.000000000 + x = 1.885768398 + 1.642857143
x = 1.885768398 + 1.642857143

Combine like terms: 1.885768398 + 1.642857143 = 3.528625541
x = 3.528625541

Simplifying
x = 3.528625541

Subproblem 2
x + -1.642857143 = -1.885768398

Simplifying
x + -1.642857143 = -1.885768398

Reorder the terms:
-1.642857143 + x = -1.885768398

Solving
-1.642857143 + x = -1.885768398

Solving for variable 'x'.

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

Add '1.642857143' to each side of the equation.
-1.642857143 + 1.642857143 + x = -1.885768398 + 1.642857143

Combine like terms: -1.642857143 + 1.642857143 = 0.000000000
0.000000000 + x = -1.885768398 + 1.642857143
x = -1.885768398 + 1.642857143

Combine like terms: -1.885768398 + 1.642857143 = -0.242911255
x = -0.242911255

Simplifying
x = -0.242911255

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.528625541, -0.242911255}
Solution
x = {3.528625541, -0.242911255}