x^2+x-21=8x-3

Solution for x^2+x-21=8x-3 equation:

Simplifying
x2 + x + -21 = 8x + -3

Reorder the terms:
-21 + x + x2 = 8x + -3

Reorder the terms:
-21 + x + x2 = -3 + 8x

Solving
-21 + x + x2 = -3 + 8x

Solving for variable 'x'.

Reorder the terms:
-21 + 3 + x + -8x + x2 = -3 + 8x + 3 + -8x

Combine like terms: -21 + 3 = -18
-18 + x + -8x + x2 = -3 + 8x + 3 + -8x

Combine like terms: x + -8x = -7x
-18 + -7x + x2 = -3 + 8x + 3 + -8x

Reorder the terms:
-18 + -7x + x2 = -3 + 3 + 8x + -8x

Combine like terms: -3 + 3 = 0
-18 + -7x + x2 = 0 + 8x + -8x
-18 + -7x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-18 + -7x + 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}