2x(60-3x)6+15=15x+50

Solution for 2x(60-3x)6+15=15x+50 equation:

Simplifying
2x(60 + -3x) * 6 + 15 = 15x + 50

Reorder the terms for easier multiplication:
2 * 6x(60 + -3x) + 15 = 15x + 50

Multiply 2 * 6
12x(60 + -3x) + 15 = 15x + 50
(60 * 12x + -3x * 12x) + 15 = 15x + 50
(720x + -36x2) + 15 = 15x + 50

Reorder the terms:
15 + 720x + -36x2 = 15x + 50

Reorder the terms:
15 + 720x + -36x2 = 50 + 15x

Solving
15 + 720x + -36x2 = 50 + 15x

Solving for variable 'x'.

Reorder the terms:
15 + -50 + 720x + -15x + -36x2 = 50 + 15x + -50 + -15x

Combine like terms: 15 + -50 = -35
-35 + 720x + -15x + -36x2 = 50 + 15x + -50 + -15x

Combine like terms: 720x + -15x = 705x
-35 + 705x + -36x2 = 50 + 15x + -50 + -15x

Reorder the terms:
-35 + 705x + -36x2 = 50 + -50 + 15x + -15x

Combine like terms: 50 + -50 = 0
-35 + 705x + -36x2 = 0 + 15x + -15x
-35 + 705x + -36x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
-35 + 705x + -36x2 = 0

Begin completing the square.  Divide all terms by
-36 the coefficient of the squared term: 

Divide each side by '-36'.
0.9722222222 + -19.58333333x + x2 = 0

Move the constant term to the right:

Add '-0.9722222222' to each side of the equation.
0.9722222222 + -19.58333333x + -0.9722222222 + x2 = 0 + -0.9722222222

Reorder the terms:
0.9722222222 + -0.9722222222 + -19.58333333x + x2 = 0 + -0.9722222222

Combine like terms: 0.9722222222 + -0.9722222222 = 0.0000000000
0.0000000000 + -19.58333333x + x2 = 0 + -0.9722222222
-19.58333333x + x2 = 0 + -0.9722222222

Combine like terms: 0 + -0.9722222222 = -0.9722222222
-19.58333333x + x2 = -0.9722222222

The x term is -19.58333333x.  Take half its coefficient (-9.791666665).
Square it (95.87673608) and add it to both sides.

Add '95.87673608' to each side of the equation.
-19.58333333x + 95.87673608 + x2 = -0.9722222222 + 95.87673608

Reorder the terms:
95.87673608 + -19.58333333x + x2 = -0.9722222222 + 95.87673608

Combine like terms: -0.9722222222 + 95.87673608 = 94.9045138578
95.87673608 + -19.58333333x + x2 = 94.9045138578

Factor a perfect square on the left side:
(x + -9.791666665)(x + -9.791666665) = 94.9045138578

Calculate the square root of the right side: 9.741894778

Break this problem into two subproblems by setting 
(x + -9.791666665) equal to 9.741894778 and -9.741894778.

Subproblem 1
x + -9.791666665 = 9.741894778

Simplifying
x + -9.791666665 = 9.741894778

Reorder the terms:
-9.791666665 + x = 9.741894778

Solving
-9.791666665 + x = 9.741894778

Solving for variable 'x'.

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

Add '9.791666665' to each side of the equation.
-9.791666665 + 9.791666665 + x = 9.741894778 + 9.791666665

Combine like terms: -9.791666665 + 9.791666665 = 0.000000000
0.000000000 + x = 9.741894778 + 9.791666665
x = 9.741894778 + 9.791666665

Combine like terms: 9.741894778 + 9.791666665 = 19.533561443
x = 19.533561443

Simplifying
x = 19.533561443

Subproblem 2
x + -9.791666665 = -9.741894778

Simplifying
x + -9.791666665 = -9.741894778

Reorder the terms:
-9.791666665 + x = -9.741894778

Solving
-9.791666665 + x = -9.741894778

Solving for variable 'x'.

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

Add '9.791666665' to each side of the equation.
-9.791666665 + 9.791666665 + x = -9.741894778 + 9.791666665

Combine like terms: -9.791666665 + 9.791666665 = 0.000000000
0.000000000 + x = -9.741894778 + 9.791666665
x = -9.741894778 + 9.791666665

Combine like terms: -9.741894778 + 9.791666665 = 0.049771887
x = 0.049771887

Simplifying
x = 0.049771887

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.533561443, 0.049771887}