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

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

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

Reorder the terms:
4x(1 + x) + -2(x + 1) = 0
(1 * 4x + x * 4x) + -2(x + 1) = 0
(4x + 4x2) + -2(x + 1) = 0

Reorder the terms:
4x + 4x2 + -2(1 + x) = 0
4x + 4x2 + (1 * -2 + x * -2) = 0
4x + 4x2 + (-2 + -2x) = 0

Reorder the terms:
-2 + 4x + -2x + 4x2 = 0

Combine like terms: 4x + -2x = 2x
-2 + 2x + 4x2 = 0

Solving
-2 + 2x + 4x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 2.
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 + -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}