6x^2+19x-102=0

Solution for 6x^2+19x-102=0 equation:

Simplifying
6x2 + 19x + -102 = 0

Reorder the terms:
-102 + 19x + 6x2 = 0

Solving
-102 + 19x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -1x)(17 + -6x) = 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 '(17 + -6x)' equal to zero and attempt to solve:

Simplifying
17 + -6x = 0

Solving
17 + -6x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -6x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -6x = 0 + -17
-6x = 0 + -17

Combine like terms: 0 + -17 = -17
-6x = -17

Divide each side by '-6'.
x = 2.833333333

Simplifying
x = 2.833333333
Solution
x = {-6, 2.833333333}