3x(5x-240)=15

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Solution for 3x(5x-240)=15 equation: 


Simplifying
3x(5x + -240) = 15

Reorder the terms:
3x(-240 + 5x) = 15
(-240 * 3x + 5x * 3x) = 15
(-720x + 15x2) = 15

Solving
-720x + 15x2 = 15

Solving for variable 'x'.

Reorder the terms:
-15 + -720x + 15x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -720x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(-1 + -48x + x2) = 0

Ignore the factor 15.

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

Simplifying
-1 + -48x + x2 = 0

Solving
-1 + -48x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -48x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -48x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -48x + x2 = 0 + 1
-48x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-48x + x2 = 1

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 = 1 + 576

Reorder the terms:
576 + -48x + x2 = 1 + 576

Combine like terms: 1 + 576 = 577
576 + -48x + x2 = 577

Factor a perfect square on the left side:
(x + -24)(x + -24) = 577

Calculate the square root of the right side: 24.020824299

Break this problem into two subproblems by setting 
(x + -24) equal to 24.020824299 and -24.020824299.


Subproblem 1
x + -24 = 24.020824299

Simplifying
x + -24 = 24.020824299

Reorder the terms:
-24 + x = 24.020824299

Solving
-24 + x = 24.020824299

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 = 24.020824299 + 24

Combine like terms: -24 + 24 = 0
0 + x = 24.020824299 + 24
x = 24.020824299 + 24

Combine like terms: 24.020824299 + 24 = 48.020824299
x = 48.020824299

Simplifying
x = 48.020824299


Subproblem 2
x + -24 = -24.020824299

Simplifying
x + -24 = -24.020824299

Reorder the terms:
-24 + x = -24.020824299

Solving
-24 + x = -24.020824299

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 = -24.020824299 + 24

Combine like terms: -24 + 24 = 0
0 + x = -24.020824299 + 24
x = -24.020824299 + 24

Combine like terms: -24.020824299 + 24 = -0.020824299
x = -0.020824299

Simplifying
x = -0.020824299


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {48.020824299, -0.020824299}
Solution
x = {48.020824299, -0.020824299}

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