(3x-45)*2x=14-6x

Solution for (3x-45)*2x=14-6x equation:

Simplifying
(3x + -45) * 2x = 14 + -6x

Reorder the terms:
(-45 + 3x) * 2x = 14 + -6x

Reorder the terms for easier multiplication:
2x(-45 + 3x) = 14 + -6x
(-45 * 2x + 3x * 2x) = 14 + -6x
(-90x + 6x2) = 14 + -6x

Solving
-90x + 6x2 = 14 + -6x

Solving for variable 'x'.

Reorder the terms:
-14 + -90x + 6x + 6x2 = 14 + -6x + -14 + 6x

Combine like terms: -90x + 6x = -84x
-14 + -84x + 6x2 = 14 + -6x + -14 + 6x

Reorder the terms:
-14 + -84x + 6x2 = 14 + -14 + -6x + 6x

Combine like terms: 14 + -14 = 0
-14 + -84x + 6x2 = 0 + -6x + 6x
-14 + -84x + 6x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-14 + -84x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -42x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -42x + 3x2)' equal to zero and attempt to solve:

Simplifying
-7 + -42x + 3x2 = 0

Solving
-7 + -42x + 3x2 = 0

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

Divide each side by '3'.
-2.333333333 + -14x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -14x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -14x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -14x + x2 = 0 + 2.333333333
-14x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-14x + x2 = 2.333333333

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = 2.333333333 + 49

Reorder the terms:
49 + -14x + x2 = 2.333333333 + 49

Combine like terms: 2.333333333 + 49 = 51.333333333
49 + -14x + x2 = 51.333333333

Factor a perfect square on the left side:
(x + -7)(x + -7) = 51.333333333

Calculate the square root of the right side: 7.16472842

Break this problem into two subproblems by setting 
(x + -7) equal to 7.16472842 and -7.16472842.

Subproblem 1
x + -7 = 7.16472842

Simplifying
x + -7 = 7.16472842

Reorder the terms:
-7 + x = 7.16472842

Solving
-7 + x = 7.16472842

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 7.16472842 + 7

Combine like terms: -7 + 7 = 0
0 + x = 7.16472842 + 7
x = 7.16472842 + 7

Combine like terms: 7.16472842 + 7 = 14.16472842
x = 14.16472842

Simplifying
x = 14.16472842

Subproblem 2
x + -7 = -7.16472842

Simplifying
x + -7 = -7.16472842

Reorder the terms:
-7 + x = -7.16472842

Solving
-7 + x = -7.16472842

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -7.16472842 + 7

Combine like terms: -7 + 7 = 0
0 + x = -7.16472842 + 7
x = -7.16472842 + 7

Combine like terms: -7.16472842 + 7 = -0.16472842
x = -0.16472842

Simplifying
x = -0.16472842

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.16472842, -0.16472842}
Solution
x = {14.16472842, -0.16472842}