3(42x-3)+32x(4+7x)=12

Solution for 3(42x-3)+32x(4+7x)=12 equation:

Simplifying
3(42x + -3) + 32x(4 + 7x) = 12

Reorder the terms:
3(-3 + 42x) + 32x(4 + 7x) = 12
(-3 * 3 + 42x * 3) + 32x(4 + 7x) = 12
(-9 + 126x) + 32x(4 + 7x) = 12
-9 + 126x + (4 * 32x + 7x * 32x) = 12
-9 + 126x + (128x + 224x2) = 12

Combine like terms: 126x + 128x = 254x
-9 + 254x + 224x2 = 12

Solving
-9 + 254x + 224x2 = 12

Solving for variable 'x'.

Reorder the terms:
-9 + -12 + 254x + 224x2 = 12 + -12

Combine like terms: -9 + -12 = -21
-21 + 254x + 224x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-21 + 254x + 224x2 = 0

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

Divide each side by '224'.
-0.09375 + 1.133928571x + x2 = 0

Move the constant term to the right:

Add '0.09375' to each side of the equation.
-0.09375 + 1.133928571x + 0.09375 + x2 = 0 + 0.09375

Reorder the terms:
-0.09375 + 0.09375 + 1.133928571x + x2 = 0 + 0.09375

Combine like terms: -0.09375 + 0.09375 = 0.00000
0.00000 + 1.133928571x + x2 = 0 + 0.09375
1.133928571x + x2 = 0 + 0.09375

Combine like terms: 0 + 0.09375 = 0.09375
1.133928571x + x2 = 0.09375

The x term is 1.133928571x.  Take half its coefficient (0.5669642855).
Square it (0.3214485010) and add it to both sides.

Add '0.3214485010' to each side of the equation.
1.133928571x + 0.3214485010 + x2 = 0.09375 + 0.3214485010

Reorder the terms:
0.3214485010 + 1.133928571x + x2 = 0.09375 + 0.3214485010

Combine like terms: 0.09375 + 0.3214485010 = 0.415198501
0.3214485010 + 1.133928571x + x2 = 0.415198501

Factor a perfect square on the left side:
(x + 0.5669642855)(x + 0.5669642855) = 0.415198501

Calculate the square root of the right side: 0.644358985

Break this problem into two subproblems by setting 
(x + 0.5669642855) equal to 0.644358985 and -0.644358985.

Subproblem 1
x + 0.5669642855 = 0.644358985

Simplifying
x + 0.5669642855 = 0.644358985

Reorder the terms:
0.5669642855 + x = 0.644358985

Solving
0.5669642855 + x = 0.644358985

Solving for variable 'x'.

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

Add '-0.5669642855' to each side of the equation.
0.5669642855 + -0.5669642855 + x = 0.644358985 + -0.5669642855

Combine like terms: 0.5669642855 + -0.5669642855 = 0.0000000000
0.0000000000 + x = 0.644358985 + -0.5669642855
x = 0.644358985 + -0.5669642855

Combine like terms: 0.644358985 + -0.5669642855 = 0.0773946995
x = 0.0773946995

Simplifying
x = 0.0773946995

Subproblem 2
x + 0.5669642855 = -0.644358985

Simplifying
x + 0.5669642855 = -0.644358985

Reorder the terms:
0.5669642855 + x = -0.644358985

Solving
0.5669642855 + x = -0.644358985

Solving for variable 'x'.

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

Add '-0.5669642855' to each side of the equation.
0.5669642855 + -0.5669642855 + x = -0.644358985 + -0.5669642855

Combine like terms: 0.5669642855 + -0.5669642855 = 0.0000000000
0.0000000000 + x = -0.644358985 + -0.5669642855
x = -0.644358985 + -0.5669642855

Combine like terms: -0.644358985 + -0.5669642855 = -1.2113232705
x = -1.2113232705

Simplifying
x = -1.2113232705

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.0773946995, -1.2113232705}