x^2-13x+43=3

Solution for x^2-13x+43=3 equation:

Simplifying
x2 + -13x + 43 = 3

Reorder the terms:
43 + -13x + x2 = 3

Solving
43 + -13x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
43 + -3 + -13x + x2 = 3 + -3

Combine like terms: 43 + -3 = 40
40 + -13x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
40 + -13x + x2 = 0

Factor a trinomial.
(5 + -1x)(8 + -1x) = 0

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
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
Solution
x = {5, 8}