600=(21-2x)(34-2x)

Solution for 600=(21-2x)(34-2x) equation:

Simplifying
600 = (21 + -2x)(34 + -2x)

Multiply (21 + -2x) * (34 + -2x)
600 = (21(34 + -2x) + -2x * (34 + -2x))
600 = ((34 * 21 + -2x * 21) + -2x * (34 + -2x))
600 = ((714 + -42x) + -2x * (34 + -2x))
600 = (714 + -42x + (34 * -2x + -2x * -2x))
600 = (714 + -42x + (-68x + 4x2))

Combine like terms: -42x + -68x = -110x
600 = (714 + -110x + 4x2)

Solving
600 = 714 + -110x + 4x2

Solving for variable 'x'.

Combine like terms: 600 + -714 = -114
-114 + 110x + -4x2 = 714 + -110x + 4x2 + -714 + 110x + -4x2

Reorder the terms:
-114 + 110x + -4x2 = 714 + -714 + -110x + 110x + 4x2 + -4x2

Combine like terms: 714 + -714 = 0
-114 + 110x + -4x2 = 0 + -110x + 110x + 4x2 + -4x2
-114 + 110x + -4x2 = -110x + 110x + 4x2 + -4x2

Combine like terms: -110x + 110x = 0
-114 + 110x + -4x2 = 0 + 4x2 + -4x2
-114 + 110x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-114 + 110x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-57 + 55x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-57 + 55x + -2x2)' equal to zero and attempt to solve:

Simplifying
-57 + 55x + -2x2 = 0

Solving
-57 + 55x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
28.5 + -27.5x + x2 = 0

Move the constant term to the right:

Add '-28.5' to each side of the equation.
28.5 + -27.5x + -28.5 + x2 = 0 + -28.5

Reorder the terms:
28.5 + -28.5 + -27.5x + x2 = 0 + -28.5

Combine like terms: 28.5 + -28.5 = 0.0
0.0 + -27.5x + x2 = 0 + -28.5
-27.5x + x2 = 0 + -28.5

Combine like terms: 0 + -28.5 = -28.5
-27.5x + x2 = -28.5

The x term is -27.5x.  Take half its coefficient (-13.75).
Square it (189.0625) and add it to both sides.

Add '189.0625' to each side of the equation.
-27.5x + 189.0625 + x2 = -28.5 + 189.0625

Reorder the terms:
189.0625 + -27.5x + x2 = -28.5 + 189.0625

Combine like terms: -28.5 + 189.0625 = 160.5625
189.0625 + -27.5x + x2 = 160.5625

Factor a perfect square on the left side:
(x + -13.75)(x + -13.75) = 160.5625

Calculate the square root of the right side: 12.671325897

Break this problem into two subproblems by setting 
(x + -13.75) equal to 12.671325897 and -12.671325897.

Subproblem 1
x + -13.75 = 12.671325897

Simplifying
x + -13.75 = 12.671325897

Reorder the terms:
-13.75 + x = 12.671325897

Solving
-13.75 + x = 12.671325897

Solving for variable 'x'.

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

Add '13.75' to each side of the equation.
-13.75 + 13.75 + x = 12.671325897 + 13.75

Combine like terms: -13.75 + 13.75 = 0.00
0.00 + x = 12.671325897 + 13.75
x = 12.671325897 + 13.75

Combine like terms: 12.671325897 + 13.75 = 26.421325897
x = 26.421325897

Simplifying
x = 26.421325897

Subproblem 2
x + -13.75 = -12.671325897

Simplifying
x + -13.75 = -12.671325897

Reorder the terms:
-13.75 + x = -12.671325897

Solving
-13.75 + x = -12.671325897

Solving for variable 'x'.

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

Add '13.75' to each side of the equation.
-13.75 + 13.75 + x = -12.671325897 + 13.75

Combine like terms: -13.75 + 13.75 = 0.00
0.00 + x = -12.671325897 + 13.75
x = -12.671325897 + 13.75

Combine like terms: -12.671325897 + 13.75 = 1.078674103
x = 1.078674103

Simplifying
x = 1.078674103

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {26.421325897, 1.078674103}
Solution
x = {26.421325897, 1.078674103}