4x(x+1)=-1

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

Simplifying
4x(x + 1) = -1

Reorder the terms:
4x(1 + x) = -1
(1 * 4x + x * 4x) = -1
(4x + 4x2) = -1

Solving
4x + 4x2 = -1

Solving for variable 'x'.

Reorder the terms:
1 + 4x + 4x2 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + 4x + 4x2 = 0

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

Subproblem 1
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
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 = {-0.5, -0.5}