x^2-6x+19=5x+1

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Solution for x^2-6x+19=5x+1 equation: 


Simplifying
x2 + -6x + 19 = 5x + 1

Reorder the terms:
19 + -6x + x2 = 5x + 1

Reorder the terms:
19 + -6x + x2 = 1 + 5x

Solving
19 + -6x + x2 = 1 + 5x

Solving for variable 'x'.

Reorder the terms:
19 + -1 + -6x + -5x + x2 = 1 + 5x + -1 + -5x

Combine like terms: 19 + -1 = 18
18 + -6x + -5x + x2 = 1 + 5x + -1 + -5x

Combine like terms: -6x + -5x = -11x
18 + -11x + x2 = 1 + 5x + -1 + -5x

Reorder the terms:
18 + -11x + x2 = 1 + -1 + 5x + -5x

Combine like terms: 1 + -1 = 0
18 + -11x + x2 = 0 + 5x + -5x
18 + -11x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
18 + -11x + x2 = 0

Factor a trinomial.
(2 + -1x)(9 + -1x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {2, 9}

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