(x+48)(3x)=1260

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Solution for (x+48)(3x)=1260 equation: 


Simplifying
(x + 48)(3x) = 1260

Reorder the terms:
(48 + x)(3x) = 1260

Remove parenthesis around (3x)
(48 + x) * 3x = 1260

Reorder the terms for easier multiplication:
3x(48 + x) = 1260
(48 * 3x + x * 3x) = 1260
(144x + 3x2) = 1260

Solving
144x + 3x2 = 1260

Solving for variable 'x'.

Reorder the terms:
-1260 + 144x + 3x2 = 1260 + -1260

Combine like terms: 1260 + -1260 = 0
-1260 + 144x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-420 + 48x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-420 + 48x + x2)' equal to zero and attempt to solve:

Simplifying
-420 + 48x + x2 = 0

Solving
-420 + 48x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '420' to each side of the equation.
-420 + 48x + 420 + x2 = 0 + 420

Reorder the terms:
-420 + 420 + 48x + x2 = 0 + 420

Combine like terms: -420 + 420 = 0
0 + 48x + x2 = 0 + 420
48x + x2 = 0 + 420

Combine like terms: 0 + 420 = 420
48x + x2 = 420

The x term is 48x.  Take half its coefficient (24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
48x + 576 + x2 = 420 + 576

Reorder the terms:
576 + 48x + x2 = 420 + 576

Combine like terms: 420 + 576 = 996
576 + 48x + x2 = 996

Factor a perfect square on the left side:
(x + 24)(x + 24) = 996

Calculate the square root of the right side: 31.559467676

Break this problem into two subproblems by setting 
(x + 24) equal to 31.559467676 and -31.559467676.


Subproblem 1
x + 24 = 31.559467676

Simplifying
x + 24 = 31.559467676

Reorder the terms:
24 + x = 31.559467676

Solving
24 + x = 31.559467676

Solving for variable 'x'.

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

Add '-24' to each side of the equation.
24 + -24 + x = 31.559467676 + -24

Combine like terms: 24 + -24 = 0
0 + x = 31.559467676 + -24
x = 31.559467676 + -24

Combine like terms: 31.559467676 + -24 = 7.559467676
x = 7.559467676

Simplifying
x = 7.559467676


Subproblem 2
x + 24 = -31.559467676

Simplifying
x + 24 = -31.559467676

Reorder the terms:
24 + x = -31.559467676

Solving
24 + x = -31.559467676

Solving for variable 'x'.

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

Add '-24' to each side of the equation.
24 + -24 + x = -31.559467676 + -24

Combine like terms: 24 + -24 = 0
0 + x = -31.559467676 + -24
x = -31.559467676 + -24

Combine like terms: -31.559467676 + -24 = -55.559467676
x = -55.559467676

Simplifying
x = -55.559467676


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.559467676, -55.559467676}
Solution
x = {7.559467676, -55.559467676}

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