0=(13x-39)(13-39x)

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Solution for 0=(13x-39)(13-39x) equation: 


Simplifying
0 = (13x + -39)(13 + -39x)

Reorder the terms:
0 = (-39 + 13x)(13 + -39x)

Multiply (-39 + 13x) * (13 + -39x)
0 = (-39(13 + -39x) + 13x * (13 + -39x))
0 = ((13 * -39 + -39x * -39) + 13x * (13 + -39x))
0 = ((-507 + 1521x) + 13x * (13 + -39x))
0 = (-507 + 1521x + (13 * 13x + -39x * 13x))
0 = (-507 + 1521x + (169x + -507x2))

Combine like terms: 1521x + 169x = 1690x
0 = (-507 + 1690x + -507x2)

Solving
0 = -507 + 1690x + -507x2

Solving for variable 'x'.

Combine like terms: 0 + 507 = 507
507 + -1690x + 507x2 = -507 + 1690x + -507x2 + 507 + -1690x + 507x2

Reorder the terms:
507 + -1690x + 507x2 = -507 + 507 + 1690x + -1690x + -507x2 + 507x2

Combine like terms: -507 + 507 = 0
507 + -1690x + 507x2 = 0 + 1690x + -1690x + -507x2 + 507x2
507 + -1690x + 507x2 = 1690x + -1690x + -507x2 + 507x2

Combine like terms: 1690x + -1690x = 0
507 + -1690x + 507x2 = 0 + -507x2 + 507x2
507 + -1690x + 507x2 = -507x2 + 507x2

Combine like terms: -507x2 + 507x2 = 0
507 + -1690x + 507x2 = 0

Factor out the Greatest Common Factor (GCF), '169'.
169(3 + -10x + 3x2) = 0

Factor a trinomial.
169((1 + -3x)(3 + -1x)) = 0

Ignore the factor 169.

Subproblem 1
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

Subproblem 2
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
Solution
x = {0.3333333333, 3}

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