2x^2-52x-1974=0

Solution for 2x^2-52x-1974=0 equation:

Simplifying
2x2 + -52x + -1974 = 0

Reorder the terms:
-1974 + -52x + 2x2 = 0

Solving
-1974 + -52x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-987 + -26x + x2) = 0

Factor a trinomial.
2((-21 + -1x)(47 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-21 + -1x)' equal to zero and attempt to solve:

Simplifying
-21 + -1x = 0

Solving
-21 + -1x = 0

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

Add '21' to each side of the equation.
-21 + 21 + -1x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -1x = 0 + 21
-1x = 0 + 21

Combine like terms: 0 + 21 = 21
-1x = 21

Divide each side by '-1'.
x = -21

Simplifying
x = -21
Subproblem 2
Set the factor '(47 + -1x)' equal to zero and attempt to solve:

Simplifying
47 + -1x = 0

Solving
47 + -1x = 0

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

Add '-47' to each side of the equation.
47 + -47 + -1x = 0 + -47

Combine like terms: 47 + -47 = 0
0 + -1x = 0 + -47
-1x = 0 + -47

Combine like terms: 0 + -47 = -47
-1x = -47

Divide each side by '-1'.
x = 47

Simplifying
x = 47
Solution
x = {-21, 47}