2(4x-3)3(2x+4)=5(2x+10)

Solution for 2(4x-3)3(2x+4)=5(2x+10) equation:

Simplifying
2(4x + -3) * 3(2x + 4) = 5(2x + 10)

Reorder the terms:
2(-3 + 4x) * 3(2x + 4) = 5(2x + 10)

Reorder the terms:
2(-3 + 4x) * 3(4 + 2x) = 5(2x + 10)

Reorder the terms for easier multiplication:
2 * 3(-3 + 4x)(4 + 2x) = 5(2x + 10)

Multiply 2 * 3
6(-3 + 4x)(4 + 2x) = 5(2x + 10)

Multiply (-3 + 4x) * (4 + 2x)
6(-3(4 + 2x) + 4x * (4 + 2x)) = 5(2x + 10)
6((4 * -3 + 2x * -3) + 4x * (4 + 2x)) = 5(2x + 10)
6((-12 + -6x) + 4x * (4 + 2x)) = 5(2x + 10)
6(-12 + -6x + (4 * 4x + 2x * 4x)) = 5(2x + 10)
6(-12 + -6x + (16x + 8x2)) = 5(2x + 10)

Combine like terms: -6x + 16x = 10x
6(-12 + 10x + 8x2) = 5(2x + 10)
(-12 * 6 + 10x * 6 + 8x2 * 6) = 5(2x + 10)
(-72 + 60x + 48x2) = 5(2x + 10)

Reorder the terms:
-72 + 60x + 48x2 = 5(10 + 2x)
-72 + 60x + 48x2 = (10 * 5 + 2x * 5)
-72 + 60x + 48x2 = (50 + 10x)

Solving
-72 + 60x + 48x2 = 50 + 10x

Solving for variable 'x'.

Reorder the terms:
-72 + -50 + 60x + -10x + 48x2 = 50 + 10x + -50 + -10x

Combine like terms: -72 + -50 = -122
-122 + 60x + -10x + 48x2 = 50 + 10x + -50 + -10x

Combine like terms: 60x + -10x = 50x
-122 + 50x + 48x2 = 50 + 10x + -50 + -10x

Reorder the terms:
-122 + 50x + 48x2 = 50 + -50 + 10x + -10x

Combine like terms: 50 + -50 = 0
-122 + 50x + 48x2 = 0 + 10x + -10x
-122 + 50x + 48x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-122 + 50x + 48x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-61 + 25x + 24x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-61 + 25x + 24x2)' equal to zero and attempt to solve:

Simplifying
-61 + 25x + 24x2 = 0

Solving
-61 + 25x + 24x2 = 0

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

Divide each side by '24'.
-2.541666667 + 1.041666667x + x2 = 0

Move the constant term to the right:

Add '2.541666667' to each side of the equation.
-2.541666667 + 1.041666667x + 2.541666667 + x2 = 0 + 2.541666667

Reorder the terms:
-2.541666667 + 2.541666667 + 1.041666667x + x2 = 0 + 2.541666667

Combine like terms: -2.541666667 + 2.541666667 = 0.000000000
0.000000000 + 1.041666667x + x2 = 0 + 2.541666667
1.041666667x + x2 = 0 + 2.541666667

Combine like terms: 0 + 2.541666667 = 2.541666667
1.041666667x + x2 = 2.541666667

The x term is 1.041666667x.  Take half its coefficient (0.5208333335).
Square it (0.2712673613) and add it to both sides.

Add '0.2712673613' to each side of the equation.
1.041666667x + 0.2712673613 + x2 = 2.541666667 + 0.2712673613

Reorder the terms:
0.2712673613 + 1.041666667x + x2 = 2.541666667 + 0.2712673613

Combine like terms: 2.541666667 + 0.2712673613 = 2.8129340283
0.2712673613 + 1.041666667x + x2 = 2.8129340283

Factor a perfect square on the left side:
(x + 0.5208333335)(x + 0.5208333335) = 2.8129340283

Calculate the square root of the right side: 1.67718038

Break this problem into two subproblems by setting 
(x + 0.5208333335) equal to 1.67718038 and -1.67718038.

Subproblem 1
x + 0.5208333335 = 1.67718038

Simplifying
x + 0.5208333335 = 1.67718038

Reorder the terms:
0.5208333335 + x = 1.67718038

Solving
0.5208333335 + x = 1.67718038

Solving for variable 'x'.

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

Add '-0.5208333335' to each side of the equation.
0.5208333335 + -0.5208333335 + x = 1.67718038 + -0.5208333335

Combine like terms: 0.5208333335 + -0.5208333335 = 0.0000000000
0.0000000000 + x = 1.67718038 + -0.5208333335
x = 1.67718038 + -0.5208333335

Combine like terms: 1.67718038 + -0.5208333335 = 1.1563470465
x = 1.1563470465

Simplifying
x = 1.1563470465

Subproblem 2
x + 0.5208333335 = -1.67718038

Simplifying
x + 0.5208333335 = -1.67718038

Reorder the terms:
0.5208333335 + x = -1.67718038

Solving
0.5208333335 + x = -1.67718038

Solving for variable 'x'.

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

Add '-0.5208333335' to each side of the equation.
0.5208333335 + -0.5208333335 + x = -1.67718038 + -0.5208333335

Combine like terms: 0.5208333335 + -0.5208333335 = 0.0000000000
0.0000000000 + x = -1.67718038 + -0.5208333335
x = -1.67718038 + -0.5208333335

Combine like terms: -1.67718038 + -0.5208333335 = -2.1980137135
x = -2.1980137135

Simplifying
x = -2.1980137135

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1563470465, -2.1980137135}
Solution
x = {1.1563470465, -2.1980137135}