(x+1)(x+1)+x^2=25

Solution for (x+1)(x+1)+x^2=25 equation:

Simplifying
(x + 1)(x + 1) + x2 = 25

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

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

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

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

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

Solving
1 + 2x + 2x2 = 25

Solving for variable 'x'.

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + x + x2) = 0

Factor a trinomial.
2((-4 + -1x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
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 = {-4, 3}