4.5(x+1)2(x+1)=0

Solution for 4.5(x+1)2(x+1)=0 equation:

Simplifying
4.5(x + 1) * 2(x + 1) = 0

Reorder the terms:
4.5(1 + x) * 2(x + 1) = 0

Reorder the terms:
4.5(1 + x) * 2(1 + x) = 0

Reorder the terms for easier multiplication:
4.5 * 2(1 + x)(1 + x) = 0

Multiply 4.5 * 2
9(1 + x)(1 + x) = 0

Multiply (1 + x) * (1 + x)
9(1(1 + x) + x(1 + x)) = 0
9((1 * 1 + x * 1) + x(1 + x)) = 0
9((1 + 1x) + x(1 + x)) = 0
9(1 + 1x + (1 * x + x * x)) = 0
9(1 + 1x + (1x + x2)) = 0

Combine like terms: 1x + 1x = 2x
9(1 + 2x + x2) = 0
(1 * 9 + 2x * 9 + x2 * 9) = 0
(9 + 18x + 9x2) = 0

Solving
9 + 18x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(1 + 2x + x2) = 0

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

Ignore the factor 9.
Subproblem 1
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
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 = {-1, -1}