7x^2-13x-102=0

Solution for 7x^2-13x-102=0 equation:

Simplifying
7x2 + -13x + -102 = 0

Reorder the terms:
-102 + -13x + 7x2 = 0

Solving
-102 + -13x + 7x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -1x)(34 + -7x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(34 + -7x)' equal to zero and attempt to solve:

Simplifying
34 + -7x = 0

Solving
34 + -7x = 0

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

Add '-34' to each side of the equation.
34 + -34 + -7x = 0 + -34

Combine like terms: 34 + -34 = 0
0 + -7x = 0 + -34
-7x = 0 + -34

Combine like terms: 0 + -34 = -34
-7x = -34

Divide each side by '-7'.
x = 4.857142857

Simplifying
x = 4.857142857
Solution
x = {-3, 4.857142857}