2x^2+100x-102=0

Solution for 2x^2+100x-102=0 equation:

Simplifying
2x2 + 100x + -102 = 0

Reorder the terms:
-102 + 100x + 2x2 = 0

Solving
-102 + 100x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-51 + 50x + x2) = 0

Factor a trinomial.
2((-51 + -1x)(1 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-51 + -1x)' equal to zero and attempt to solve:

Simplifying
-51 + -1x = 0

Solving
-51 + -1x = 0

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

Add '51' to each side of the equation.
-51 + 51 + -1x = 0 + 51

Combine like terms: -51 + 51 = 0
0 + -1x = 0 + 51
-1x = 0 + 51

Combine like terms: 0 + 51 = 51
-1x = 51

Divide each side by '-1'.
x = -51

Simplifying
x = -51
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-51, 1}