21x=8x^2-9

Solution for 21x=8x^2-9 equation:

Simplifying
21x = 8x2 + -9

Reorder the terms:
21x = -9 + 8x2

Solving
21x = -9 + 8x2

Solving for variable 'x'.

Reorder the terms:
9 + 21x + -8x2 = -9 + 8x2 + 9 + -8x2

Reorder the terms:
9 + 21x + -8x2 = -9 + 9 + 8x2 + -8x2

Combine like terms: -9 + 9 = 0
9 + 21x + -8x2 = 0 + 8x2 + -8x2
9 + 21x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
9 + 21x + -8x2 = 0

Factor a trinomial.
(3 + -1x)(3 + 8x) = 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 '(3 + 8x)' equal to zero and attempt to solve:

Simplifying
3 + 8x = 0

Solving
3 + 8x = 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 + 8x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8x = 0 + -3
8x = 0 + -3

Combine like terms: 0 + -3 = -3
8x = -3

Divide each side by '8'.
x = -0.375

Simplifying
x = -0.375
Solution
x = {3, -0.375}