x^2-4x+19=5x-1

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Solution for x^2-4x+19=5x-1 equation: 


Simplifying
x2 + -4x + 19 = 5x + -1

Reorder the terms:
19 + -4x + x2 = 5x + -1

Reorder the terms:
19 + -4x + x2 = -1 + 5x

Solving
19 + -4x + x2 = -1 + 5x

Solving for variable 'x'.

Reorder the terms:
19 + 1 + -4x + -5x + x2 = -1 + 5x + 1 + -5x

Combine like terms: 19 + 1 = 20
20 + -4x + -5x + x2 = -1 + 5x + 1 + -5x

Combine like terms: -4x + -5x = -9x
20 + -9x + x2 = -1 + 5x + 1 + -5x

Reorder the terms:
20 + -9x + x2 = -1 + 1 + 5x + -5x

Combine like terms: -1 + 1 = 0
20 + -9x + x2 = 0 + 5x + -5x
20 + -9x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
20 + -9x + x2 = 0

Factor a trinomial.
(4 + -1x)(5 + -1x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
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
Solution
x = {4, 5}

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