25x^2-50x-25=50

Solution for 25x^2-50x-25=50 equation:

Simplifying
25x2 + -50x + -25 = 50

Reorder the terms:
-25 + -50x + 25x2 = 50

Solving
-25 + -50x + 25x2 = 50

Solving for variable 'x'.

Reorder the terms:
-25 + -50 + -50x + 25x2 = 50 + -50

Combine like terms: -25 + -50 = -75
-75 + -50x + 25x2 = 50 + -50

Combine like terms: 50 + -50 = 0
-75 + -50x + 25x2 = 0

Factor out the Greatest Common Factor (GCF), '25'.
25(-3 + -2x + x2) = 0

Factor a trinomial.
25((-1 + -1x)(3 + -1x)) = 0

Ignore the factor 25.
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 '(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 = {-1, 3}