2x^2+28x-102=0

Solution for 2x^2+28x-102=0 equation:

Simplifying
2x2 + 28x + -102 = 0

Reorder the terms:
-102 + 28x + 2x2 = 0

Solving
-102 + 28x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-51 + 14x + x2) = 0

Factor a trinomial.
2((-17 + -1x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + -1x)' equal to zero and attempt to solve:

Simplifying
-17 + -1x = 0

Solving
-17 + -1x = 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 + -1x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1x = 0 + 17
-1x = 0 + 17

Combine like terms: 0 + 17 = 17
-1x = 17

Divide each side by '-1'.
x = -17

Simplifying
x = -17
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 = {-17, 3}