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

Subproblem 1
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
Subproblem 2
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
Solution
x = {-4.857142857, 3}