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

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

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

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

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

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

Multiply (-3 + 2x) * (7 + -2x)
12(-3(7 + -2x) + 2x * (7 + -2x)) = 30
12((7 * -3 + -2x * -3) + 2x * (7 + -2x)) = 30
12((-21 + 6x) + 2x * (7 + -2x)) = 30
12(-21 + 6x + (7 * 2x + -2x * 2x)) = 30
12(-21 + 6x + (14x + -4x2)) = 30

Combine like terms: 6x + 14x = 20x
12(-21 + 20x + -4x2) = 30
(-21 * 12 + 20x * 12 + -4x2 * 12) = 30
(-252 + 240x + -48x2) = 30

Solving
-252 + 240x + -48x2 = 30

Solving for variable 'x'.

Reorder the terms:
-252 + -30 + 240x + -48x2 = 30 + -30

Combine like terms: -252 + -30 = -282
-282 + 240x + -48x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-282 + 240x + -48x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-47 + 40x + -8x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-47 + 40x + -8x2)' equal to zero and attempt to solve:

Simplifying
-47 + 40x + -8x2 = 0

Solving
-47 + 40x + -8x2 = 0

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

Divide each side by '-8'.
5.875 + -5x + x2 = 0

Move the constant term to the right:

Add '-5.875' to each side of the equation.
5.875 + -5x + -5.875 + x2 = 0 + -5.875

Reorder the terms:
5.875 + -5.875 + -5x + x2 = 0 + -5.875

Combine like terms: 5.875 + -5.875 = 0.000
0.000 + -5x + x2 = 0 + -5.875
-5x + x2 = 0 + -5.875

Combine like terms: 0 + -5.875 = -5.875
-5x + x2 = -5.875

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -5.875 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -5.875 + 6.25

Combine like terms: -5.875 + 6.25 = 0.375
6.25 + -5x + x2 = 0.375

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 0.375

Calculate the square root of the right side: 0.612372436

Break this problem into two subproblems by setting 
(x + -2.5) equal to 0.612372436 and -0.612372436.

Subproblem 1
x + -2.5 = 0.612372436

Simplifying
x + -2.5 = 0.612372436

Reorder the terms:
-2.5 + x = 0.612372436

Solving
-2.5 + x = 0.612372436

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 0.612372436 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 0.612372436 + 2.5
x = 0.612372436 + 2.5

Combine like terms: 0.612372436 + 2.5 = 3.112372436
x = 3.112372436

Simplifying
x = 3.112372436

Subproblem 2
x + -2.5 = -0.612372436

Simplifying
x + -2.5 = -0.612372436

Reorder the terms:
-2.5 + x = -0.612372436

Solving
-2.5 + x = -0.612372436

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -0.612372436 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -0.612372436 + 2.5
x = -0.612372436 + 2.5

Combine like terms: -0.612372436 + 2.5 = 1.887627564
x = 1.887627564

Simplifying
x = 1.887627564

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.112372436, 1.887627564}
Solution
x = {3.112372436, 1.887627564}