4(x+1)5(x+2)=

Solution for 4(x+1)5(x+2)= equation:

Simplifying
4(x + 1) * 5(x + 2) = 0

Reorder the terms:
4(1 + x) * 5(x + 2) = 0

Reorder the terms:
4(1 + x) * 5(2 + x) = 0

Reorder the terms for easier multiplication:
4 * 5(1 + x)(2 + x) = 0

Multiply 4 * 5
20(1 + x)(2 + x) = 0

Multiply (1 + x) * (2 + x)
20(1(2 + x) + x(2 + x)) = 0
20((2 * 1 + x * 1) + x(2 + x)) = 0
20((2 + 1x) + x(2 + x)) = 0
20(2 + 1x + (2 * x + x * x)) = 0
20(2 + 1x + (2x + x2)) = 0

Combine like terms: 1x + 2x = 3x
20(2 + 3x + x2) = 0
(2 * 20 + 3x * 20 + x2 * 20) = 0
(40 + 60x + 20x2) = 0

Solving
40 + 60x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '20'.
20(2 + 3x + x2) = 0

Factor a trinomial.
20((2 + x)(1 + x)) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
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 = {-2, -1}