600=3(x-6)(2.5x-6)

Solution for 600=3(x-6)(2.5x-6) equation:

Simplifying
600 = 3(x + -6)(2.5x + -6)

Reorder the terms:
600 = 3(-6 + x)(2.5x + -6)

Reorder the terms:
600 = 3(-6 + x)(-6 + 2.5x)

Multiply (-6 + x) * (-6 + 2.5x)
600 = 3(-6(-6 + 2.5x) + x(-6 + 2.5x))
600 = 3((-6 * -6 + 2.5x * -6) + x(-6 + 2.5x))
600 = 3((36 + -15x) + x(-6 + 2.5x))
600 = 3(36 + -15x + (-6 * x + 2.5x * x))
600 = 3(36 + -15x + (-6x + 2.5x2))

Combine like terms: -15x + -6x = -21x
600 = 3(36 + -21x + 2.5x2)
600 = (36 * 3 + -21x * 3 + 2.5x2 * 3)
600 = (108 + -63x + 7.5x2)

Solving
600 = 108 + -63x + 7.5x2

Solving for variable 'x'.

Combine like terms: 600 + -108 = 492
492 + 63x + -7.5x2 = 108 + -63x + 7.5x2 + -108 + 63x + -7.5x2

Reorder the terms:
492 + 63x + -7.5x2 = 108 + -108 + -63x + 63x + 7.5x2 + -7.5x2

Combine like terms: 108 + -108 = 0
492 + 63x + -7.5x2 = 0 + -63x + 63x + 7.5x2 + -7.5x2
492 + 63x + -7.5x2 = -63x + 63x + 7.5x2 + -7.5x2

Combine like terms: -63x + 63x = 0
492 + 63x + -7.5x2 = 0 + 7.5x2 + -7.5x2
492 + 63x + -7.5x2 = 7.5x2 + -7.5x2

Combine like terms: 7.5x2 + -7.5x2 = 0.0
492 + 63x + -7.5x2 = 0.0

Begin completing the square.  Divide all terms by
-7.5 the coefficient of the squared term: 

Divide each side by '-7.5'.
-65.6 + -8.4x + x2 = 0

Move the constant term to the right:

Add '65.6' to each side of the equation.
-65.6 + -8.4x + 65.6 + x2 = 0 + 65.6

Reorder the terms:
-65.6 + 65.6 + -8.4x + x2 = 0 + 65.6

Combine like terms: -65.6 + 65.6 = 0.0
0.0 + -8.4x + x2 = 0 + 65.6
-8.4x + x2 = 0 + 65.6

Combine like terms: 0 + 65.6 = 65.6
-8.4x + x2 = 65.6

The x term is -8.4x.  Take half its coefficient (-4.2).
Square it (17.64) and add it to both sides.

Add '17.64' to each side of the equation.
-8.4x + 17.64 + x2 = 65.6 + 17.64

Reorder the terms:
17.64 + -8.4x + x2 = 65.6 + 17.64

Combine like terms: 65.6 + 17.64 = 83.24
17.64 + -8.4x + x2 = 83.24

Factor a perfect square on the left side:
(x + -4.2)(x + -4.2) = 83.24

Calculate the square root of the right side: 9.123595782

Break this problem into two subproblems by setting 
(x + -4.2) equal to 9.123595782 and -9.123595782.

Subproblem 1
x + -4.2 = 9.123595782

Simplifying
x + -4.2 = 9.123595782

Reorder the terms:
-4.2 + x = 9.123595782

Solving
-4.2 + x = 9.123595782

Solving for variable 'x'.

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

Add '4.2' to each side of the equation.
-4.2 + 4.2 + x = 9.123595782 + 4.2

Combine like terms: -4.2 + 4.2 = 0.0
0.0 + x = 9.123595782 + 4.2
x = 9.123595782 + 4.2

Combine like terms: 9.123595782 + 4.2 = 13.323595782
x = 13.323595782

Simplifying
x = 13.323595782

Subproblem 2
x + -4.2 = -9.123595782

Simplifying
x + -4.2 = -9.123595782

Reorder the terms:
-4.2 + x = -9.123595782

Solving
-4.2 + x = -9.123595782

Solving for variable 'x'.

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

Add '4.2' to each side of the equation.
-4.2 + 4.2 + x = -9.123595782 + 4.2

Combine like terms: -4.2 + 4.2 = 0.0
0.0 + x = -9.123595782 + 4.2
x = -9.123595782 + 4.2

Combine like terms: -9.123595782 + 4.2 = -4.923595782
x = -4.923595782

Simplifying
x = -4.923595782

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.323595782, -4.923595782}