72+-24x(6x-3)=5-1(x+5)

Solution for 72+-24x(6x-3)=5-1(x+5) equation:

Simplifying
72 + -24x(6x + -3) = 5 + -1(x + 5)

Reorder the terms:
72 + -24x(-3 + 6x) = 5 + -1(x + 5)
72 + (-3 * -24x + 6x * -24x) = 5 + -1(x + 5)
72 + (72x + -144x2) = 5 + -1(x + 5)

Reorder the terms:
72 + 72x + -144x2 = 5 + -1(5 + x)
72 + 72x + -144x2 = 5 + (5 * -1 + x * -1)
72 + 72x + -144x2 = 5 + (-5 + -1x)

Combine like terms: 5 + -5 = 0
72 + 72x + -144x2 = 0 + -1x
72 + 72x + -144x2 = -1x

Solving
72 + 72x + -144x2 = -1x

Solving for variable 'x'.

Reorder the terms:
72 + 72x + x + -144x2 = -1x + x

Combine like terms: 72x + x = 73x
72 + 73x + -144x2 = -1x + x

Combine like terms: -1x + x = 0
72 + 73x + -144x2 = 0

Begin completing the square.  Divide all terms by
-144 the coefficient of the squared term: 

Divide each side by '-144'.
-0.5 + -0.5069444444x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.5069444444x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.5069444444x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.5069444444x + x2 = 0 + 0.5
-0.5069444444x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.5069444444x + x2 = 0.5

The x term is -0.5069444444x.  Take half its coefficient (-0.2534722222).
Square it (0.06424816743) and add it to both sides.

Add '0.06424816743' to each side of the equation.
-0.5069444444x + 0.06424816743 + x2 = 0.5 + 0.06424816743

Reorder the terms:
0.06424816743 + -0.5069444444x + x2 = 0.5 + 0.06424816743

Combine like terms: 0.5 + 0.06424816743 = 0.56424816743
0.06424816743 + -0.5069444444x + x2 = 0.56424816743

Factor a perfect square on the left side:
(x + -0.2534722222)(x + -0.2534722222) = 0.56424816743

Calculate the square root of the right side: 0.751164541

Break this problem into two subproblems by setting 
(x + -0.2534722222) equal to 0.751164541 and -0.751164541.

Subproblem 1
x + -0.2534722222 = 0.751164541

Simplifying
x + -0.2534722222 = 0.751164541

Reorder the terms:
-0.2534722222 + x = 0.751164541

Solving
-0.2534722222 + x = 0.751164541

Solving for variable 'x'.

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

Add '0.2534722222' to each side of the equation.
-0.2534722222 + 0.2534722222 + x = 0.751164541 + 0.2534722222

Combine like terms: -0.2534722222 + 0.2534722222 = 0.0000000000
0.0000000000 + x = 0.751164541 + 0.2534722222
x = 0.751164541 + 0.2534722222

Combine like terms: 0.751164541 + 0.2534722222 = 1.0046367632
x = 1.0046367632

Simplifying
x = 1.0046367632

Subproblem 2
x + -0.2534722222 = -0.751164541

Simplifying
x + -0.2534722222 = -0.751164541

Reorder the terms:
-0.2534722222 + x = -0.751164541

Solving
-0.2534722222 + x = -0.751164541

Solving for variable 'x'.

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

Add '0.2534722222' to each side of the equation.
-0.2534722222 + 0.2534722222 + x = -0.751164541 + 0.2534722222

Combine like terms: -0.2534722222 + 0.2534722222 = 0.0000000000
0.0000000000 + x = -0.751164541 + 0.2534722222
x = -0.751164541 + 0.2534722222

Combine like terms: -0.751164541 + 0.2534722222 = -0.4976923188
x = -0.4976923188

Simplifying
x = -0.4976923188

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0046367632, -0.4976923188}