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

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

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

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

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

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

Combine like terms: 4x + 1x = 5x
(1 + 5x + 4x2) = 0

Solving
1 + 5x + 4x2 = 0

Solving for variable 'x'.

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

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 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {-1, -0.25}