5(4+2x)1(8x-12)=68

Solution for 5(4+2x)1(8x-12)=68 equation:

Simplifying
5(4 + 2x) * 1(8x + -12) = 68

Reorder the terms:
5(4 + 2x) * 1(-12 + 8x) = 68

Reorder the terms for easier multiplication:
5 * 1(4 + 2x)(-12 + 8x) = 68

Multiply 5 * 1
5(4 + 2x)(-12 + 8x) = 68

Multiply (4 + 2x) * (-12 + 8x)
5(4(-12 + 8x) + 2x * (-12 + 8x)) = 68
5((-12 * 4 + 8x * 4) + 2x * (-12 + 8x)) = 68
5((-48 + 32x) + 2x * (-12 + 8x)) = 68
5(-48 + 32x + (-12 * 2x + 8x * 2x)) = 68
5(-48 + 32x + (-24x + 16x2)) = 68

Combine like terms: 32x + -24x = 8x
5(-48 + 8x + 16x2) = 68
(-48 * 5 + 8x * 5 + 16x2 * 5) = 68
(-240 + 40x + 80x2) = 68

Solving
-240 + 40x + 80x2 = 68

Solving for variable 'x'.

Reorder the terms:
-240 + -68 + 40x + 80x2 = 68 + -68

Combine like terms: -240 + -68 = -308
-308 + 40x + 80x2 = 68 + -68

Combine like terms: 68 + -68 = 0
-308 + 40x + 80x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-77 + 10x + 20x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-77 + 10x + 20x2)' equal to zero and attempt to solve:

Simplifying
-77 + 10x + 20x2 = 0

Solving
-77 + 10x + 20x2 = 0

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

Divide each side by '20'.
-3.85 + 0.5x + x2 = 0.0

Move the constant term to the right:

Add '3.85' to each side of the equation.
-3.85 + 0.5x + 3.85 + x2 = 0.0 + 3.85

Reorder the terms:
-3.85 + 3.85 + 0.5x + x2 = 0.0 + 3.85

Combine like terms: -3.85 + 3.85 = 0.00
0.00 + 0.5x + x2 = 0.0 + 3.85
0.5x + x2 = 0.0 + 3.85

Combine like terms: 0.0 + 3.85 = 3.85
0.5x + x2 = 3.85

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 3.85 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 3.85 + 0.0625

Combine like terms: 3.85 + 0.0625 = 3.9125
0.0625 + 0.5x + x2 = 3.9125

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 3.9125

Calculate the square root of the right side: 1.978004044

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.978004044 and -1.978004044.

Subproblem 1
x + 0.25 = 1.978004044

Simplifying
x + 0.25 = 1.978004044

Reorder the terms:
0.25 + x = 1.978004044

Solving
0.25 + x = 1.978004044

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 1.978004044 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 1.978004044 + -0.25
x = 1.978004044 + -0.25

Combine like terms: 1.978004044 + -0.25 = 1.728004044
x = 1.728004044

Simplifying
x = 1.728004044

Subproblem 2
x + 0.25 = -1.978004044

Simplifying
x + 0.25 = -1.978004044

Reorder the terms:
0.25 + x = -1.978004044

Solving
0.25 + x = -1.978004044

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -1.978004044 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -1.978004044 + -0.25
x = -1.978004044 + -0.25

Combine like terms: -1.978004044 + -0.25 = -2.228004044
x = -2.228004044

Simplifying
x = -2.228004044

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.728004044, -2.228004044}
Solution
x = {1.728004044, -2.228004044}