3x^2-48x+135=0

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Solution for 3x^2-48x+135=0 equation: 


Simplifying
3x2 + -48x + 135 = 0

Reorder the terms:
135 + -48x + 3x2 = 0

Solving
135 + -48x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(45 + -16x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(45 + -16x + x2)' equal to zero and attempt to solve:

Simplifying
45 + -16x + x2 = 0

Solving
45 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + -16x + -45 + x2 = 0 + -45

Reorder the terms:
45 + -45 + -16x + x2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -16x + x2 = 0 + -45
-16x + x2 = 0 + -45

Combine like terms: 0 + -45 = -45
-16x + x2 = -45

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -45 + 64

Reorder the terms:
64 + -16x + x2 = -45 + 64

Combine like terms: -45 + 64 = 19
64 + -16x + x2 = 19

Factor a perfect square on the left side:
(x + -8)(x + -8) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(x + -8) equal to 4.358898944 and -4.358898944.


Subproblem 1
x + -8 = 4.358898944

Simplifying
x + -8 = 4.358898944

Reorder the terms:
-8 + x = 4.358898944

Solving
-8 + x = 4.358898944

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 4.358898944 + 8

Combine like terms: -8 + 8 = 0
0 + x = 4.358898944 + 8
x = 4.358898944 + 8

Combine like terms: 4.358898944 + 8 = 12.358898944
x = 12.358898944

Simplifying
x = 12.358898944


Subproblem 2
x + -8 = -4.358898944

Simplifying
x + -8 = -4.358898944

Reorder the terms:
-8 + x = -4.358898944

Solving
-8 + x = -4.358898944

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -4.358898944 + 8

Combine like terms: -8 + 8 = 0
0 + x = -4.358898944 + 8
x = -4.358898944 + 8

Combine like terms: -4.358898944 + 8 = 3.641101056
x = 3.641101056

Simplifying
x = 3.641101056


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.358898944, 3.641101056}
Solution
x = {12.358898944, 3.641101056}

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