(x+1)(x+1)=25

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

Simplifying
(x + 1)(x + 1) = 25

Reorder the terms:
(1 + x)(x + 1) = 25

Reorder the terms:
(1 + x)(1 + x) = 25

Multiply (1 + x) * (1 + x)
(1(1 + x) + x(1 + x)) = 25
((1 * 1 + x * 1) + x(1 + x)) = 25
((1 + 1x) + x(1 + x)) = 25
(1 + 1x + (1 * x + x * x)) = 25
(1 + 1x + (1x + x2)) = 25

Combine like terms: 1x + 1x = 2x
(1 + 2x + x2) = 25

Solving
1 + 2x + x2 = 25

Solving for variable 'x'.

Reorder the terms:
1 + -25 + 2x + x2 = 25 + -25

Combine like terms: 1 + -25 = -24
-24 + 2x + x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-24 + 2x + x2 = 0

Factor a trinomial.
(-6 + -1x)(4 + -1x) = 0

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

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-6, 4}