3(2x-2)4(7-2x)=30

Solution for 3(2x-2)4(7-2x)=30 equation:

Simplifying
3(2x + -2) * 4(7 + -2x) = 30

Reorder the terms:
3(-2 + 2x) * 4(7 + -2x) = 30

Reorder the terms for easier multiplication:
3 * 4(-2 + 2x)(7 + -2x) = 30

Multiply 3 * 4
12(-2 + 2x)(7 + -2x) = 30

Multiply (-2 + 2x) * (7 + -2x)
12(-2(7 + -2x) + 2x * (7 + -2x)) = 30
12((7 * -2 + -2x * -2) + 2x * (7 + -2x)) = 30
12((-14 + 4x) + 2x * (7 + -2x)) = 30
12(-14 + 4x + (7 * 2x + -2x * 2x)) = 30
12(-14 + 4x + (14x + -4x2)) = 30

Combine like terms: 4x + 14x = 18x
12(-14 + 18x + -4x2) = 30
(-14 * 12 + 18x * 12 + -4x2 * 12) = 30
(-168 + 216x + -48x2) = 30

Solving
-168 + 216x + -48x2 = 30

Solving for variable 'x'.

Reorder the terms:
-168 + -30 + 216x + -48x2 = 30 + -30

Combine like terms: -168 + -30 = -198
-198 + 216x + -48x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-198 + 216x + -48x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-33 + 36x + -8x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-33 + 36x + -8x2)' equal to zero and attempt to solve:

Simplifying
-33 + 36x + -8x2 = 0

Solving
-33 + 36x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
4.125 + -4.5x + x2 = 0

Move the constant term to the right:

Add '-4.125' to each side of the equation.
4.125 + -4.5x + -4.125 + x2 = 0 + -4.125

Reorder the terms:
4.125 + -4.125 + -4.5x + x2 = 0 + -4.125

Combine like terms: 4.125 + -4.125 = 0.000
0.000 + -4.5x + x2 = 0 + -4.125
-4.5x + x2 = 0 + -4.125

Combine like terms: 0 + -4.125 = -4.125
-4.5x + x2 = -4.125

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = -4.125 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = -4.125 + 5.0625

Combine like terms: -4.125 + 5.0625 = 0.9375
5.0625 + -4.5x + x2 = 0.9375

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 0.9375

Calculate the square root of the right side: 0.968245837

Break this problem into two subproblems by setting 
(x + -2.25) equal to 0.968245837 and -0.968245837.

Subproblem 1
x + -2.25 = 0.968245837

Simplifying
x + -2.25 = 0.968245837

Reorder the terms:
-2.25 + x = 0.968245837

Solving
-2.25 + x = 0.968245837

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 0.968245837 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 0.968245837 + 2.25
x = 0.968245837 + 2.25

Combine like terms: 0.968245837 + 2.25 = 3.218245837
x = 3.218245837

Simplifying
x = 3.218245837

Subproblem 2
x + -2.25 = -0.968245837

Simplifying
x + -2.25 = -0.968245837

Reorder the terms:
-2.25 + x = -0.968245837

Solving
-2.25 + x = -0.968245837

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -0.968245837 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -0.968245837 + 2.25
x = -0.968245837 + 2.25

Combine like terms: -0.968245837 + 2.25 = 1.281754163
x = 1.281754163

Simplifying
x = 1.281754163

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.218245837, 1.281754163}
Solution
x = {3.218245837, 1.281754163}