4(2x+1)(x+1)=0

Solution for 4(2x+1)(x+1)=0 equation:

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

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

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

Multiply (1 + 2x) * (1 + x)
4(1(1 + x) + 2x * (1 + x)) = 0
4((1 * 1 + x * 1) + 2x * (1 + x)) = 0
4((1 + 1x) + 2x * (1 + x)) = 0
4(1 + 1x + (1 * 2x + x * 2x)) = 0
4(1 + 1x + (2x + 2x2)) = 0

Combine like terms: 1x + 2x = 3x
4(1 + 3x + 2x2) = 0
(1 * 4 + 3x * 4 + 2x2 * 4) = 0
(4 + 12x + 8x2) = 0

Solving
4 + 12x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 3x + 2x2) = 0

Factor a trinomial.
4((1 + x)(1 + 2x)) = 0

Ignore the factor 4.
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 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-1, -0.5}