(x+1)(x+1)-64=0

Solution for (x+1)(x+1)-64=0 equation:

Simplifying
(x + 1)(x + 1) + -64 = 0

Reorder the terms:
(1 + x)(x + 1) + -64 = 0

Reorder the terms:
(1 + x)(1 + x) + -64 = 0

Multiply (1 + x) * (1 + x)
(1(1 + x) + x(1 + x)) + -64 = 0
((1 * 1 + x * 1) + x(1 + x)) + -64 = 0
((1 + 1x) + x(1 + x)) + -64 = 0
(1 + 1x + (1 * x + x * x)) + -64 = 0
(1 + 1x + (1x + x2)) + -64 = 0

Combine like terms: 1x + 1x = 2x
(1 + 2x + x2) + -64 = 0

Reorder the terms:
1 + -64 + 2x + x2 = 0

Combine like terms: 1 + -64 = -63
-63 + 2x + x2 = 0

Solving
-63 + 2x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + -1x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-9, 7}