5(3x-8)1(4x+6)+3=72

Solution for 5(3x-8)1(4x+6)+3=72 equation:

Simplifying
5(3x + -8) * 1(4x + 6) + 3 = 72

Reorder the terms:
5(-8 + 3x) * 1(4x + 6) + 3 = 72

Reorder the terms:
5(-8 + 3x) * 1(6 + 4x) + 3 = 72

Reorder the terms for easier multiplication:
5 * 1(-8 + 3x)(6 + 4x) + 3 = 72

Multiply 5 * 1
5(-8 + 3x)(6 + 4x) + 3 = 72

Multiply (-8 + 3x) * (6 + 4x)
5(-8(6 + 4x) + 3x * (6 + 4x)) + 3 = 72
5((6 * -8 + 4x * -8) + 3x * (6 + 4x)) + 3 = 72
5((-48 + -32x) + 3x * (6 + 4x)) + 3 = 72
5(-48 + -32x + (6 * 3x + 4x * 3x)) + 3 = 72
5(-48 + -32x + (18x + 12x2)) + 3 = 72

Combine like terms: -32x + 18x = -14x
5(-48 + -14x + 12x2) + 3 = 72
(-48 * 5 + -14x * 5 + 12x2 * 5) + 3 = 72
(-240 + -70x + 60x2) + 3 = 72

Reorder the terms:
-240 + 3 + -70x + 60x2 = 72

Combine like terms: -240 + 3 = -237
-237 + -70x + 60x2 = 72

Solving
-237 + -70x + 60x2 = 72

Solving for variable 'x'.

Reorder the terms:
-237 + -72 + -70x + 60x2 = 72 + -72

Combine like terms: -237 + -72 = -309
-309 + -70x + 60x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-309 + -70x + 60x2 = 0

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

Divide each side by '60'.
-5.15 + -1.166666667x + x2 = 0.0

Move the constant term to the right:

Add '5.15' to each side of the equation.
-5.15 + -1.166666667x + 5.15 + x2 = 0.0 + 5.15

Reorder the terms:
-5.15 + 5.15 + -1.166666667x + x2 = 0.0 + 5.15

Combine like terms: -5.15 + 5.15 = 0.00
0.00 + -1.166666667x + x2 = 0.0 + 5.15
-1.166666667x + x2 = 0.0 + 5.15

Combine like terms: 0.0 + 5.15 = 5.15
-1.166666667x + x2 = 5.15

The x term is -1.166666667x.  Take half its coefficient (-0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
-1.166666667x + 0.3402777780 + x2 = 5.15 + 0.3402777780

Reorder the terms:
0.3402777780 + -1.166666667x + x2 = 5.15 + 0.3402777780

Combine like terms: 5.15 + 0.3402777780 = 5.490277778
0.3402777780 + -1.166666667x + x2 = 5.490277778

Factor a perfect square on the left side:
(x + -0.5833333335)(x + -0.5833333335) = 5.490277778

Calculate the square root of the right side: 2.343134178

Break this problem into two subproblems by setting 
(x + -0.5833333335) equal to 2.343134178 and -2.343134178.

Subproblem 1
x + -0.5833333335 = 2.343134178

Simplifying
x + -0.5833333335 = 2.343134178

Reorder the terms:
-0.5833333335 + x = 2.343134178

Solving
-0.5833333335 + x = 2.343134178

Solving for variable 'x'.

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

Add '0.5833333335' to each side of the equation.
-0.5833333335 + 0.5833333335 + x = 2.343134178 + 0.5833333335

Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000
0.0000000000 + x = 2.343134178 + 0.5833333335
x = 2.343134178 + 0.5833333335

Combine like terms: 2.343134178 + 0.5833333335 = 2.9264675115
x = 2.9264675115

Simplifying
x = 2.9264675115

Subproblem 2
x + -0.5833333335 = -2.343134178

Simplifying
x + -0.5833333335 = -2.343134178

Reorder the terms:
-0.5833333335 + x = -2.343134178

Solving
-0.5833333335 + x = -2.343134178

Solving for variable 'x'.

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

Add '0.5833333335' to each side of the equation.
-0.5833333335 + 0.5833333335 + x = -2.343134178 + 0.5833333335

Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000
0.0000000000 + x = -2.343134178 + 0.5833333335
x = -2.343134178 + 0.5833333335

Combine like terms: -2.343134178 + 0.5833333335 = -1.7598008445
x = -1.7598008445

Simplifying
x = -1.7598008445

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.9264675115, -1.7598008445}