x^2-3x+19=6x+1

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Solution for x^2-3x+19=6x+1 equation: 


Simplifying
x2 + -3x + 19 = 6x + 1

Reorder the terms:
19 + -3x + x2 = 6x + 1

Reorder the terms:
19 + -3x + x2 = 1 + 6x

Solving
19 + -3x + x2 = 1 + 6x

Solving for variable 'x'.

Reorder the terms:
19 + -1 + -3x + -6x + x2 = 1 + 6x + -1 + -6x

Combine like terms: 19 + -1 = 18
18 + -3x + -6x + x2 = 1 + 6x + -1 + -6x

Combine like terms: -3x + -6x = -9x
18 + -9x + x2 = 1 + 6x + -1 + -6x

Reorder the terms:
18 + -9x + x2 = 1 + -1 + 6x + -6x

Combine like terms: 1 + -1 = 0
18 + -9x + x2 = 0 + 6x + -6x
18 + -9x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
18 + -9x + x2 = 0

Factor a trinomial.
(3 + -1x)(6 + -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 '(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 = {3, 6}

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