15x(x-60)=30

Solution for 15x(x-60)=30 equation:

Simplifying
15x(x + -60) = 30

Reorder the terms:
15x(-60 + x) = 30
(-60 * 15x + x * 15x) = 30
(-900x + 15x2) = 30

Solving
-900x + 15x2 = 30

Solving for variable 'x'.

Reorder the terms:
-30 + -900x + 15x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -900x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(-2 + -60x + x2) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(-2 + -60x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + -60x + x2 = 0

Solving
-2 + -60x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -60x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -60x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -60x + x2 = 0 + 2
-60x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-60x + x2 = 2

The x term is -60x.  Take half its coefficient (-30).
Square it (900) and add it to both sides.

Add '900' to each side of the equation.
-60x + 900 + x2 = 2 + 900

Reorder the terms:
900 + -60x + x2 = 2 + 900

Combine like terms: 2 + 900 = 902
900 + -60x + x2 = 902

Factor a perfect square on the left side:
(x + -30)(x + -30) = 902

Calculate the square root of the right side: 30.033314835

Break this problem into two subproblems by setting 
(x + -30) equal to 30.033314835 and -30.033314835.

Subproblem 1
x + -30 = 30.033314835

Simplifying
x + -30 = 30.033314835

Reorder the terms:
-30 + x = 30.033314835

Solving
-30 + x = 30.033314835

Solving for variable 'x'.

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

Add '30' to each side of the equation.
-30 + 30 + x = 30.033314835 + 30

Combine like terms: -30 + 30 = 0
0 + x = 30.033314835 + 30
x = 30.033314835 + 30

Combine like terms: 30.033314835 + 30 = 60.033314835
x = 60.033314835

Simplifying
x = 60.033314835

Subproblem 2
x + -30 = -30.033314835

Simplifying
x + -30 = -30.033314835

Reorder the terms:
-30 + x = -30.033314835

Solving
-30 + x = -30.033314835

Solving for variable 'x'.

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

Add '30' to each side of the equation.
-30 + 30 + x = -30.033314835 + 30

Combine like terms: -30 + 30 = 0
0 + x = -30.033314835 + 30
x = -30.033314835 + 30

Combine like terms: -30.033314835 + 30 = -0.033314835
x = -0.033314835

Simplifying
x = -0.033314835

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {60.033314835, -0.033314835}
Solution
x = {60.033314835, -0.033314835}