x^2+14x-1976=0

Solution for x^2+14x-1976=0 equation:

Simplifying
x2 + 14x + -1976 = 0

Reorder the terms:
-1976 + 14x + x2 = 0

Solving
-1976 + 14x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-52 + -1x)(38 + -1x) = 0

Subproblem 1
Set the factor '(-52 + -1x)' equal to zero and attempt to solve:

Simplifying
-52 + -1x = 0

Solving
-52 + -1x = 0

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

Add '52' to each side of the equation.
-52 + 52 + -1x = 0 + 52

Combine like terms: -52 + 52 = 0
0 + -1x = 0 + 52
-1x = 0 + 52

Combine like terms: 0 + 52 = 52
-1x = 52

Divide each side by '-1'.
x = -52

Simplifying
x = -52
Subproblem 2
Set the factor '(38 + -1x)' equal to zero and attempt to solve:

Simplifying
38 + -1x = 0

Solving
38 + -1x = 0

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

Add '-38' to each side of the equation.
38 + -38 + -1x = 0 + -38

Combine like terms: 38 + -38 = 0
0 + -1x = 0 + -38
-1x = 0 + -38

Combine like terms: 0 + -38 = -38
-1x = -38

Divide each side by '-1'.
x = 38

Simplifying
x = 38
Solution
x = {-52, 38}