x(4x+5)=-1

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

Simplifying
x(4x + 5) = -1

Reorder the terms:
x(5 + 4x) = -1
(5 * x + 4x * x) = -1
(5x + 4x2) = -1

Solving
5x + 4x2 = -1

Solving for variable 'x'.

Reorder the terms:
1 + 5x + 4x2 = -1 + 1

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

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}