(x+3)(x+3)-30=6

Solution for (x+3)(x+3)-30=6 equation:

Simplifying
(x + 3)(x + 3) + -30 = 6

Reorder the terms:
(3 + x)(x + 3) + -30 = 6

Reorder the terms:
(3 + x)(3 + x) + -30 = 6

Multiply (3 + x) * (3 + x)
(3(3 + x) + x(3 + x)) + -30 = 6
((3 * 3 + x * 3) + x(3 + x)) + -30 = 6
((9 + 3x) + x(3 + x)) + -30 = 6
(9 + 3x + (3 * x + x * x)) + -30 = 6
(9 + 3x + (3x + x2)) + -30 = 6

Combine like terms: 3x + 3x = 6x
(9 + 6x + x2) + -30 = 6

Reorder the terms:
9 + -30 + 6x + x2 = 6

Combine like terms: 9 + -30 = -21
-21 + 6x + x2 = 6

Solving
-21 + 6x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
-21 + -6 + 6x + x2 = 6 + -6

Combine like terms: -21 + -6 = -27
-27 + 6x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-27 + 6x + x2 = 0

Factor a trinomial.
(-9 + -1x)(3 + -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 '(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 = {-9, 3}