(12-2x)(20-x)=114

Solution for (12-2x)(20-x)=114 equation:

Simplifying
(12 + -2x)(20 + -1x) = 114

Multiply (12 + -2x) * (20 + -1x)
(12(20 + -1x) + -2x * (20 + -1x)) = 114
((20 * 12 + -1x * 12) + -2x * (20 + -1x)) = 114
((240 + -12x) + -2x * (20 + -1x)) = 114
(240 + -12x + (20 * -2x + -1x * -2x)) = 114
(240 + -12x + (-40x + 2x2)) = 114

Combine like terms: -12x + -40x = -52x
(240 + -52x + 2x2) = 114

Solving
240 + -52x + 2x2 = 114

Solving for variable 'x'.

Reorder the terms:
240 + -114 + -52x + 2x2 = 114 + -114

Combine like terms: 240 + -114 = 126
126 + -52x + 2x2 = 114 + -114

Combine like terms: 114 + -114 = 0
126 + -52x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(63 + -26x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(63 + -26x + x2)' equal to zero and attempt to solve:

Simplifying
63 + -26x + x2 = 0

Solving
63 + -26x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-63' to each side of the equation.
63 + -26x + -63 + x2 = 0 + -63

Reorder the terms:
63 + -63 + -26x + x2 = 0 + -63

Combine like terms: 63 + -63 = 0
0 + -26x + x2 = 0 + -63
-26x + x2 = 0 + -63

Combine like terms: 0 + -63 = -63
-26x + x2 = -63

The x term is -26x.  Take half its coefficient (-13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
-26x + 169 + x2 = -63 + 169

Reorder the terms:
169 + -26x + x2 = -63 + 169

Combine like terms: -63 + 169 = 106
169 + -26x + x2 = 106

Factor a perfect square on the left side:
(x + -13)(x + -13) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(x + -13) equal to 10.295630141 and -10.295630141.

Subproblem 1
x + -13 = 10.295630141

Simplifying
x + -13 = 10.295630141

Reorder the terms:
-13 + x = 10.295630141

Solving
-13 + x = 10.295630141

Solving for variable 'x'.

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

Add '13' to each side of the equation.
-13 + 13 + x = 10.295630141 + 13

Combine like terms: -13 + 13 = 0
0 + x = 10.295630141 + 13
x = 10.295630141 + 13

Combine like terms: 10.295630141 + 13 = 23.295630141
x = 23.295630141

Simplifying
x = 23.295630141

Subproblem 2
x + -13 = -10.295630141

Simplifying
x + -13 = -10.295630141

Reorder the terms:
-13 + x = -10.295630141

Solving
-13 + x = -10.295630141

Solving for variable 'x'.

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

Add '13' to each side of the equation.
-13 + 13 + x = -10.295630141 + 13

Combine like terms: -13 + 13 = 0
0 + x = -10.295630141 + 13
x = -10.295630141 + 13

Combine like terms: -10.295630141 + 13 = 2.704369859
x = 2.704369859

Simplifying
x = 2.704369859

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {23.295630141, 2.704369859}
Solution
x = {23.295630141, 2.704369859}