8x^2=13x+21

Solution for 8x^2=13x+21 equation:

Simplifying
8x2 = 13x + 21

Reorder the terms:
8x2 = 21 + 13x

Solving
8x2 = 21 + 13x

Solving for variable 'x'.

Reorder the terms:
-21 + -13x + 8x2 = 21 + 13x + -21 + -13x

Reorder the terms:
-21 + -13x + 8x2 = 21 + -21 + 13x + -13x

Combine like terms: 21 + -21 = 0
-21 + -13x + 8x2 = 0 + 13x + -13x
-21 + -13x + 8x2 = 13x + -13x

Combine like terms: 13x + -13x = 0
-21 + -13x + 8x2 = 0

Factor a trinomial.
(-1 + -1x)(21 + -8x) = 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 '(21 + -8x)' equal to zero and attempt to solve:

Simplifying
21 + -8x = 0

Solving
21 + -8x = 0

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

Add '-21' to each side of the equation.
21 + -21 + -8x = 0 + -21

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

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

Divide each side by '-8'.
x = 2.625

Simplifying
x = 2.625
Solution
x = {-1, 2.625}