25x(x+1)=6

Solution for 25x(x+1)=6 equation:

Simplifying
25x(x + 1) = 6

Reorder the terms:
25x(1 + x) = 6
(1 * 25x + x * 25x) = 6
(25x + 25x2) = 6

Solving
25x + 25x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + 25x + 25x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 25x + 25x2 = 0

Factor a trinomial.
(-6 + -5x)(1 + -5x) = 0

Subproblem 1
Set the factor '(-6 + -5x)' equal to zero and attempt to solve:

Simplifying
-6 + -5x = 0

Solving
-6 + -5x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -5x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5x = 0 + 6
-5x = 0 + 6

Combine like terms: 0 + 6 = 6
-5x = 6

Divide each side by '-5'.
x = -1.2

Simplifying
x = -1.2
Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {-1.2, 0.2}