-9x^2+40x+84=0

Solution for -9x^2+40x+84=0 equation:

Simplifying
-9x2 + 40x + 84 = 0

Reorder the terms:
84 + 40x + -9x2 = 0

Solving
84 + 40x + -9x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + -1x)(14 + 9x) = 0

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(14 + 9x)' equal to zero and attempt to solve:

Simplifying
14 + 9x = 0

Solving
14 + 9x = 0

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

Add '-14' to each side of the equation.
14 + -14 + 9x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 9x = 0 + -14
9x = 0 + -14

Combine like terms: 0 + -14 = -14
9x = -14

Divide each side by '9'.
x = -1.555555556

Simplifying
x = -1.555555556
Solution
x = {6, -1.555555556}