(24-2x)(13-2x)=242

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Solution for (24-2x)(13-2x)=242 equation: 


Simplifying
(24 + -2x)(13 + -2x) = 242

Multiply (24 + -2x) * (13 + -2x)
(24(13 + -2x) + -2x * (13 + -2x)) = 242
((13 * 24 + -2x * 24) + -2x * (13 + -2x)) = 242
((312 + -48x) + -2x * (13 + -2x)) = 242
(312 + -48x + (13 * -2x + -2x * -2x)) = 242
(312 + -48x + (-26x + 4x2)) = 242

Combine like terms: -48x + -26x = -74x
(312 + -74x + 4x2) = 242

Solving
312 + -74x + 4x2 = 242

Solving for variable 'x'.

Reorder the terms:
312 + -242 + -74x + 4x2 = 242 + -242

Combine like terms: 312 + -242 = 70
70 + -74x + 4x2 = 242 + -242

Combine like terms: 242 + -242 = 0
70 + -74x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(35 + -37x + 2x2) = 0

Factor a trinomial.
2((1 + -1x)(35 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 2
Set the factor '(35 + -2x)' equal to zero and attempt to solve:

Simplifying
35 + -2x = 0

Solving
35 + -2x = 0

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

Add '-35' to each side of the equation.
35 + -35 + -2x = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -2x = 0 + -35
-2x = 0 + -35

Combine like terms: 0 + -35 = -35
-2x = -35

Divide each side by '-2'.
x = 17.5

Simplifying
x = 17.5
Solution
x = {1, 17.5}

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