0=x^2-19x+78

Solution for 0=x^2-19x+78 equation:

Simplifying
0 = x2 + -19x + 78

Reorder the terms:
0 = 78 + -19x + x2

Solving
0 = 78 + -19x + x2

Solving for variable 'x'.

Combine like terms: 0 + -78 = -78
-78 + 19x + -1x2 = 78 + -19x + x2 + -78 + 19x + -1x2

Reorder the terms:
-78 + 19x + -1x2 = 78 + -78 + -19x + 19x + x2 + -1x2

Combine like terms: 78 + -78 = 0
-78 + 19x + -1x2 = 0 + -19x + 19x + x2 + -1x2
-78 + 19x + -1x2 = -19x + 19x + x2 + -1x2

Combine like terms: -19x + 19x = 0
-78 + 19x + -1x2 = 0 + x2 + -1x2
-78 + 19x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-78 + 19x + -1x2 = 0

Factor a trinomial.
(-13 + x)(6 + -1x) = 0

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

Simplifying
-13 + x = 0

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

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

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

Simplifying
x = 13
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {13, 6}