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

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


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

Multiply (8 + -2x) * (13 + -2x)
(8(13 + -2x) + -2x * (13 + -2x)) = 0
((13 * 8 + -2x * 8) + -2x * (13 + -2x)) = 0
((104 + -16x) + -2x * (13 + -2x)) = 0
(104 + -16x + (13 * -2x + -2x * -2x)) = 0
(104 + -16x + (-26x + 4x2)) = 0

Combine like terms: -16x + -26x = -42x
(104 + -42x + 4x2) = 0

Solving
104 + -42x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(52 + -21x + 2x2) = 0

Factor a trinomial.
2((4 + -1x)(13 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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

Simplifying
13 + -2x = 0

Solving
13 + -2x = 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 + -2x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2x = 0 + -13
-2x = 0 + -13

Combine like terms: 0 + -13 = -13
-2x = -13

Divide each side by '-2'.
x = 6.5

Simplifying
x = 6.5
Solution
x = {4, 6.5}

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