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((-1 + -1x)(51 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
x = {-1, 51}