x^2-5x+19=6x-5

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Solution for x^2-5x+19=6x-5 equation: 


Simplifying
x2 + -5x + 19 = 6x + -5

Reorder the terms:
19 + -5x + x2 = 6x + -5

Reorder the terms:
19 + -5x + x2 = -5 + 6x

Solving
19 + -5x + x2 = -5 + 6x

Solving for variable 'x'.

Reorder the terms:
19 + 5 + -5x + -6x + x2 = -5 + 6x + 5 + -6x

Combine like terms: 19 + 5 = 24
24 + -5x + -6x + x2 = -5 + 6x + 5 + -6x

Combine like terms: -5x + -6x = -11x
24 + -11x + x2 = -5 + 6x + 5 + -6x

Reorder the terms:
24 + -11x + x2 = -5 + 5 + 6x + -6x

Combine like terms: -5 + 5 = 0
24 + -11x + x2 = 0 + 6x + -6x
24 + -11x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
24 + -11x + x2 = 0

Factor a trinomial.
(3 + -1x)(8 + -1x) = 0


Subproblem 1
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

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 = {3, 8}

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