(x+3)(x+3)+100=676

Solution for (x+3)(x+3)+100=676 equation:

Simplifying
(x + 3)(x + 3) + 100 = 676

Reorder the terms:
(3 + x)(x + 3) + 100 = 676

Reorder the terms:
(3 + x)(3 + x) + 100 = 676

Multiply (3 + x) * (3 + x)
(3(3 + x) + x(3 + x)) + 100 = 676
((3 * 3 + x * 3) + x(3 + x)) + 100 = 676
((9 + 3x) + x(3 + x)) + 100 = 676
(9 + 3x + (3 * x + x * x)) + 100 = 676
(9 + 3x + (3x + x2)) + 100 = 676

Combine like terms: 3x + 3x = 6x
(9 + 6x + x2) + 100 = 676

Reorder the terms:
9 + 100 + 6x + x2 = 676

Combine like terms: 9 + 100 = 109
109 + 6x + x2 = 676

Solving
109 + 6x + x2 = 676

Solving for variable 'x'.

Reorder the terms:
109 + -676 + 6x + x2 = 676 + -676

Combine like terms: 109 + -676 = -567
-567 + 6x + x2 = 676 + -676

Combine like terms: 676 + -676 = 0
-567 + 6x + x2 = 0

Factor a trinomial.
(-27 + -1x)(21 + -1x) = 0

Subproblem 1
Set the factor '(-27 + -1x)' equal to zero and attempt to solve:

Simplifying
-27 + -1x = 0

Solving
-27 + -1x = 0

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

Add '27' to each side of the equation.
-27 + 27 + -1x = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -1x = 0 + 27
-1x = 0 + 27

Combine like terms: 0 + 27 = 27
-1x = 27

Divide each side by '-1'.
x = -27

Simplifying
x = -27
Subproblem 2
Set the factor '(21 + -1x)' equal to zero and attempt to solve:

Simplifying
21 + -1x = 0

Solving
21 + -1x = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1x = 0 + -21
-1x = 0 + -21

Combine like terms: 0 + -21 = -21
-1x = -21

Divide each side by '-1'.
x = 21

Simplifying
x = 21
Solution
x = {-27, 21}