(5x-48)(3x)=180

Solution for (5x-48)(3x)=180 equation:

Simplifying
(5x + -48)(3x) = 180

Reorder the terms:
(-48 + 5x)(3x) = 180

Remove parenthesis around (3x)
(-48 + 5x) * 3x = 180

Reorder the terms for easier multiplication:
3x(-48 + 5x) = 180
(-48 * 3x + 5x * 3x) = 180
(-144x + 15x2) = 180

Solving
-144x + 15x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + -144x + 15x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -144x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-60 + -48x + 5x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-60 + -48x + 5x2)' equal to zero and attempt to solve:

Simplifying
-60 + -48x + 5x2 = 0

Solving
-60 + -48x + 5x2 = 0

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

Divide each side by '5'.
-12 + -9.6x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -9.6x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -9.6x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -9.6x + x2 = 0 + 12
-9.6x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-9.6x + x2 = 12

The x term is -9.6x.  Take half its coefficient (-4.8).
Square it (23.04) and add it to both sides.

Add '23.04' to each side of the equation.
-9.6x + 23.04 + x2 = 12 + 23.04

Reorder the terms:
23.04 + -9.6x + x2 = 12 + 23.04

Combine like terms: 12 + 23.04 = 35.04
23.04 + -9.6x + x2 = 35.04

Factor a perfect square on the left side:
(x + -4.8)(x + -4.8) = 35.04

Calculate the square root of the right side: 5.919459435

Break this problem into two subproblems by setting 
(x + -4.8) equal to 5.919459435 and -5.919459435.

Subproblem 1
x + -4.8 = 5.919459435

Simplifying
x + -4.8 = 5.919459435

Reorder the terms:
-4.8 + x = 5.919459435

Solving
-4.8 + x = 5.919459435

Solving for variable 'x'.

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

Add '4.8' to each side of the equation.
-4.8 + 4.8 + x = 5.919459435 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0
0.0 + x = 5.919459435 + 4.8
x = 5.919459435 + 4.8

Combine like terms: 5.919459435 + 4.8 = 10.719459435
x = 10.719459435

Simplifying
x = 10.719459435

Subproblem 2
x + -4.8 = -5.919459435

Simplifying
x + -4.8 = -5.919459435

Reorder the terms:
-4.8 + x = -5.919459435

Solving
-4.8 + x = -5.919459435

Solving for variable 'x'.

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

Add '4.8' to each side of the equation.
-4.8 + 4.8 + x = -5.919459435 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0
0.0 + x = -5.919459435 + 4.8
x = -5.919459435 + 4.8

Combine like terms: -5.919459435 + 4.8 = -1.119459435
x = -1.119459435

Simplifying
x = -1.119459435

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.719459435, -1.119459435}
Solution
x = {10.719459435, -1.119459435}