8x^2+53x+84=0

Solution for 8x^2+53x+84=0 equation:

Simplifying
8x2 + 53x + 84 = 0

Reorder the terms:
84 + 53x + 8x2 = 0

Solving
84 + 53x + 8x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + x)(21 + 8x) = 0

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
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 = {-4, -2.625}