x^2-x+4x+16=19x+1

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Solution for x^2-x+4x+16=19x+1 equation: 


Simplifying
x2 + -1x + 4x + 16 = 19x + 1

Reorder the terms:
16 + -1x + 4x + x2 = 19x + 1

Combine like terms: -1x + 4x = 3x
16 + 3x + x2 = 19x + 1

Reorder the terms:
16 + 3x + x2 = 1 + 19x

Solving
16 + 3x + x2 = 1 + 19x

Solving for variable 'x'.

Reorder the terms:
16 + -1 + 3x + -19x + x2 = 1 + 19x + -1 + -19x

Combine like terms: 16 + -1 = 15
15 + 3x + -19x + x2 = 1 + 19x + -1 + -19x

Combine like terms: 3x + -19x = -16x
15 + -16x + x2 = 1 + 19x + -1 + -19x

Reorder the terms:
15 + -16x + x2 = 1 + -1 + 19x + -19x

Combine like terms: 1 + -1 = 0
15 + -16x + x2 = 0 + 19x + -19x
15 + -16x + x2 = 19x + -19x

Combine like terms: 19x + -19x = 0
15 + -16x + x2 = 0

Factor a trinomial.
(1 + -1x)(15 + -1x) = 0


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {1, 15}

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