14x*3x=56-18x

Solution for 14x*3x=56-18x equation:

Simplifying
14x * 3x = 56 + -18x

Reorder the terms for easier multiplication:
14 * 3x * x = 56 + -18x

Multiply 14 * 3
42x * x = 56 + -18x

Multiply x * x
42x2 = 56 + -18x

Solving
42x2 = 56 + -18x

Solving for variable 'x'.

Reorder the terms:
-56 + 18x + 42x2 = 56 + -18x + -56 + 18x

Reorder the terms:
-56 + 18x + 42x2 = 56 + -56 + -18x + 18x

Combine like terms: 56 + -56 = 0
-56 + 18x + 42x2 = 0 + -18x + 18x
-56 + 18x + 42x2 = -18x + 18x

Combine like terms: -18x + 18x = 0
-56 + 18x + 42x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + 9x + 21x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-28 + 9x + 21x2)' equal to zero and attempt to solve:

Simplifying
-28 + 9x + 21x2 = 0

Solving
-28 + 9x + 21x2 = 0

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

Divide each side by '21'.
-1.333333333 + 0.4285714286x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 0.4285714286x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 0.4285714286x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 0.4285714286x + x2 = 0 + 1.333333333
0.4285714286x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
0.4285714286x + x2 = 1.333333333

The x term is 0.4285714286x.  Take half its coefficient (0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
0.4285714286x + 0.04591836735 + x2 = 1.333333333 + 0.04591836735

Reorder the terms:
0.04591836735 + 0.4285714286x + x2 = 1.333333333 + 0.04591836735

Combine like terms: 1.333333333 + 0.04591836735 = 1.37925170035
0.04591836735 + 0.4285714286x + x2 = 1.37925170035

Factor a perfect square on the left side:
(x + 0.2142857143)(x + 0.2142857143) = 1.37925170035

Calculate the square root of the right side: 1.174415472

Break this problem into two subproblems by setting 
(x + 0.2142857143) equal to 1.174415472 and -1.174415472.

Subproblem 1
x + 0.2142857143 = 1.174415472

Simplifying
x + 0.2142857143 = 1.174415472

Reorder the terms:
0.2142857143 + x = 1.174415472

Solving
0.2142857143 + x = 1.174415472

Solving for variable 'x'.

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

Add '-0.2142857143' to each side of the equation.
0.2142857143 + -0.2142857143 + x = 1.174415472 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + x = 1.174415472 + -0.2142857143
x = 1.174415472 + -0.2142857143

Combine like terms: 1.174415472 + -0.2142857143 = 0.9601297577
x = 0.9601297577

Simplifying
x = 0.9601297577

Subproblem 2
x + 0.2142857143 = -1.174415472

Simplifying
x + 0.2142857143 = -1.174415472

Reorder the terms:
0.2142857143 + x = -1.174415472

Solving
0.2142857143 + x = -1.174415472

Solving for variable 'x'.

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

Add '-0.2142857143' to each side of the equation.
0.2142857143 + -0.2142857143 + x = -1.174415472 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + x = -1.174415472 + -0.2142857143
x = -1.174415472 + -0.2142857143

Combine like terms: -1.174415472 + -0.2142857143 = -1.3887011863
x = -1.3887011863

Simplifying
x = -1.3887011863

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9601297577, -1.3887011863}
Solution
x = {0.9601297577, -1.3887011863}