x^2-19=-8x+1

Solution for x^2-19=-8x+1 equation:

Simplifying
x2 + -19 = -8x + 1

Reorder the terms:
-19 + x2 = -8x + 1

Reorder the terms:
-19 + x2 = 1 + -8x

Solving
-19 + x2 = 1 + -8x

Solving for variable 'x'.

Reorder the terms:
-19 + -1 + 8x + x2 = 1 + -8x + -1 + 8x

Combine like terms: -19 + -1 = -20
-20 + 8x + x2 = 1 + -8x + -1 + 8x

Reorder the terms:
-20 + 8x + x2 = 1 + -1 + -8x + 8x

Combine like terms: 1 + -1 = 0
-20 + 8x + x2 = 0 + -8x + 8x
-20 + 8x + x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-20 + 8x + x2 = 0

Factor a trinomial.
(-10 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10
Subproblem 2
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
Solution
x = {-10, 2}