322x^2+126x=168x^2+42

Solution for 322x^2+126x=168x^2+42 equation:

Simplifying
322x2 + 126x = 168x2 + 42

Reorder the terms:
126x + 322x2 = 168x2 + 42

Reorder the terms:
126x + 322x2 = 42 + 168x2

Solving
126x + 322x2 = 42 + 168x2

Solving for variable 'x'.

Reorder the terms:
-42 + 126x + 322x2 + -168x2 = 42 + 168x2 + -42 + -168x2

Combine like terms: 322x2 + -168x2 = 154x2
-42 + 126x + 154x2 = 42 + 168x2 + -42 + -168x2

Reorder the terms:
-42 + 126x + 154x2 = 42 + -42 + 168x2 + -168x2

Combine like terms: 42 + -42 = 0
-42 + 126x + 154x2 = 0 + 168x2 + -168x2
-42 + 126x + 154x2 = 168x2 + -168x2

Combine like terms: 168x2 + -168x2 = 0
-42 + 126x + 154x2 = 0

Factor out the Greatest Common Factor (GCF), '14'.
14(-3 + 9x + 11x2) = 0

Ignore the factor 14.
Subproblem 1
Set the factor '(-3 + 9x + 11x2)' equal to zero and attempt to solve:

Simplifying
-3 + 9x + 11x2 = 0

Solving
-3 + 9x + 11x2 = 0

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

Divide each side by '11'.
-0.2727272727 + 0.8181818182x + x2 = 0

Move the constant term to the right:

Add '0.2727272727' to each side of the equation.
-0.2727272727 + 0.8181818182x + 0.2727272727 + x2 = 0 + 0.2727272727

Reorder the terms:
-0.2727272727 + 0.2727272727 + 0.8181818182x + x2 = 0 + 0.2727272727

Combine like terms: -0.2727272727 + 0.2727272727 = 0.0000000000
0.0000000000 + 0.8181818182x + x2 = 0 + 0.2727272727
0.8181818182x + x2 = 0 + 0.2727272727

Combine like terms: 0 + 0.2727272727 = 0.2727272727
0.8181818182x + x2 = 0.2727272727

The x term is 0.8181818182x.  Take half its coefficient (0.4090909091).
Square it (0.1673553719) and add it to both sides.

Add '0.1673553719' to each side of the equation.
0.8181818182x + 0.1673553719 + x2 = 0.2727272727 + 0.1673553719

Reorder the terms:
0.1673553719 + 0.8181818182x + x2 = 0.2727272727 + 0.1673553719

Combine like terms: 0.2727272727 + 0.1673553719 = 0.4400826446
0.1673553719 + 0.8181818182x + x2 = 0.4400826446

Factor a perfect square on the left side:
(x + 0.4090909091)(x + 0.4090909091) = 0.4400826446

Calculate the square root of the right side: 0.663387251

Break this problem into two subproblems by setting 
(x + 0.4090909091) equal to 0.663387251 and -0.663387251.

Subproblem 1
x + 0.4090909091 = 0.663387251

Simplifying
x + 0.4090909091 = 0.663387251

Reorder the terms:
0.4090909091 + x = 0.663387251

Solving
0.4090909091 + x = 0.663387251

Solving for variable 'x'.

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

Add '-0.4090909091' to each side of the equation.
0.4090909091 + -0.4090909091 + x = 0.663387251 + -0.4090909091

Combine like terms: 0.4090909091 + -0.4090909091 = 0.0000000000
0.0000000000 + x = 0.663387251 + -0.4090909091
x = 0.663387251 + -0.4090909091

Combine like terms: 0.663387251 + -0.4090909091 = 0.2542963419
x = 0.2542963419

Simplifying
x = 0.2542963419

Subproblem 2
x + 0.4090909091 = -0.663387251

Simplifying
x + 0.4090909091 = -0.663387251

Reorder the terms:
0.4090909091 + x = -0.663387251

Solving
0.4090909091 + x = -0.663387251

Solving for variable 'x'.

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

Add '-0.4090909091' to each side of the equation.
0.4090909091 + -0.4090909091 + x = -0.663387251 + -0.4090909091

Combine like terms: 0.4090909091 + -0.4090909091 = 0.0000000000
0.0000000000 + x = -0.663387251 + -0.4090909091
x = -0.663387251 + -0.4090909091

Combine like terms: -0.663387251 + -0.4090909091 = -1.0724781601
x = -1.0724781601

Simplifying
x = -1.0724781601

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2542963419, -1.0724781601}
Solution
x = {0.2542963419, -1.0724781601}