(x-13)(x-34)=0

Solution for (x-13)(x-34)=0 equation:

Simplifying
(x + -13)(x + -34) = 0

Reorder the terms:
(-13 + x)(x + -34) = 0

Reorder the terms:
(-13 + x)(-34 + x) = 0

Multiply (-13 + x) * (-34 + x)
(-13(-34 + x) + x(-34 + x)) = 0
((-34 * -13 + x * -13) + x(-34 + x)) = 0
((442 + -13x) + x(-34 + x)) = 0
(442 + -13x + (-34 * x + x * x)) = 0
(442 + -13x + (-34x + x2)) = 0

Combine like terms: -13x + -34x = -47x
(442 + -47x + x2) = 0

Solving
442 + -47x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(13 + -1x)(34 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(34 + -1x)' equal to zero and attempt to solve:

Simplifying
34 + -1x = 0

Solving
34 + -1x = 0

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

Add '-34' to each side of the equation.
34 + -34 + -1x = 0 + -34

Combine like terms: 34 + -34 = 0
0 + -1x = 0 + -34
-1x = 0 + -34

Combine like terms: 0 + -34 = -34
-1x = -34

Divide each side by '-1'.
x = 34

Simplifying
x = 34
Solution
x = {13, 34}