3x^2+32x+84=0

Solution for 3x^2+32x+84=0 equation:

Simplifying
3x2 + 32x + 84 = 0

Reorder the terms:
84 + 32x + 3x2 = 0

Solving
84 + 32x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + x)(14 + 3x) = 0

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

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
Subproblem 2
Set the factor '(14 + 3x)' equal to zero and attempt to solve:

Simplifying
14 + 3x = 0

Solving
14 + 3x = 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 + 3x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 3x = 0 + -14
3x = 0 + -14

Combine like terms: 0 + -14 = -14
3x = -14

Divide each side by '3'.
x = -4.666666667

Simplifying
x = -4.666666667
Solution
x = {-6, -4.666666667}