2(8-x)(13-x)=0

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Solution for 2(8-x)(13-x)=0 equation: 


Simplifying
2(8 + -1x)(13 + -1x) = 0

Multiply (8 + -1x) * (13 + -1x)
2(8(13 + -1x) + -1x * (13 + -1x)) = 0
2((13 * 8 + -1x * 8) + -1x * (13 + -1x)) = 0
2((104 + -8x) + -1x * (13 + -1x)) = 0
2(104 + -8x + (13 * -1x + -1x * -1x)) = 0
2(104 + -8x + (-13x + 1x2)) = 0

Combine like terms: -8x + -13x = -21x
2(104 + -21x + 1x2) = 0
(104 * 2 + -21x * 2 + 1x2 * 2) = 0
(208 + -42x + 2x2) = 0

Solving
208 + -42x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(104 + -21x + x2) = 0

Factor a trinomial.
2((8 + -1x)(13 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8

Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {8, 13}

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