-4(x+3)(x+3)=-16

Solution for -4(x+3)(x+3)=-16 equation:

Simplifying
-4(x + 3)(x + 3) = -16

Reorder the terms:
-4(3 + x)(x + 3) = -16

Reorder the terms:
-4(3 + x)(3 + x) = -16

Multiply (3 + x) * (3 + x)
-4(3(3 + x) + x(3 + x)) = -16
-4((3 * 3 + x * 3) + x(3 + x)) = -16
-4((9 + 3x) + x(3 + x)) = -16
-4(9 + 3x + (3 * x + x * x)) = -16
-4(9 + 3x + (3x + x2)) = -16

Combine like terms: 3x + 3x = 6x
-4(9 + 6x + x2) = -16
(9 * -4 + 6x * -4 + x2 * -4) = -16
(-36 + -24x + -4x2) = -16

Solving
-36 + -24x + -4x2 = -16

Solving for variable 'x'.

Reorder the terms:
-36 + 16 + -24x + -4x2 = -16 + 16

Combine like terms: -36 + 16 = -20
-20 + -24x + -4x2 = -16 + 16

Combine like terms: -16 + 16 = 0
-20 + -24x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(5 + 6x + x2) = 0

Factor a trinomial.
-4((5 + x)(1 + x)) = 0

Ignore the factor -4.
Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {-5, -1}