(50-2X)(42-2X)=1584

Solution for (50-2X)(42-2X)=1584 equation:

Simplifying
(50 + -2X)(42 + -2X) = 1584

Multiply (50 + -2X) * (42 + -2X)
(50(42 + -2X) + -2X * (42 + -2X)) = 1584
((42 * 50 + -2X * 50) + -2X * (42 + -2X)) = 1584
((2100 + -100X) + -2X * (42 + -2X)) = 1584
(2100 + -100X + (42 * -2X + -2X * -2X)) = 1584
(2100 + -100X + (-84X + 4X2)) = 1584

Combine like terms: -100X + -84X = -184X
(2100 + -184X + 4X2) = 1584

Solving
2100 + -184X + 4X2 = 1584

Solving for variable 'X'.

Reorder the terms:
2100 + -1584 + -184X + 4X2 = 1584 + -1584

Combine like terms: 2100 + -1584 = 516
516 + -184X + 4X2 = 1584 + -1584

Combine like terms: 1584 + -1584 = 0
516 + -184X + 4X2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(129 + -46X + X2) = 0

Factor a trinomial.
4((3 + -1X)(43 + -1X)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -1X)' equal to zero and attempt to solve:

Simplifying
3 + -1X = 0

Solving
3 + -1X = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1X = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1X = 0 + -3
-1X = 0 + -3

Combine like terms: 0 + -3 = -3
-1X = -3

Divide each side by '-1'.
X = 3

Simplifying
X = 3
Subproblem 2
Set the factor '(43 + -1X)' equal to zero and attempt to solve:

Simplifying
43 + -1X = 0

Solving
43 + -1X = 0

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

Add '-43' to each side of the equation.
43 + -43 + -1X = 0 + -43

Combine like terms: 43 + -43 = 0
0 + -1X = 0 + -43
-1X = 0 + -43

Combine like terms: 0 + -43 = -43
-1X = -43

Divide each side by '-1'.
X = 43

Simplifying
X = 43
Solution
X = {3, 43}