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

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

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

Reorder the terms:
4x(1 + x) + -1(x + 1) = 0
(1 * 4x + x * 4x) + -1(x + 1) = 0
(4x + 4x2) + -1(x + 1) = 0

Reorder the terms:
4x + 4x2 + -1(1 + x) = 0
4x + 4x2 + (1 * -1 + x * -1) = 0
4x + 4x2 + (-1 + -1x) = 0

Reorder the terms:
-1 + 4x + -1x + 4x2 = 0

Combine like terms: 4x + -1x = 3x
-1 + 3x + 4x2 = 0

Solving
-1 + 3x + 4x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

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

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

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

Divide each side by '-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}