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

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

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

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

Reorder the terms:
1x + 2x2 + 4(1 + 2x) = 0
1x + 2x2 + (1 * 4 + 2x * 4) = 0
1x + 2x2 + (4 + 8x) = 0

Reorder the terms:
4 + 1x + 8x + 2x2 = 0

Combine like terms: 1x + 8x = 9x
4 + 9x + 2x2 = 0

Solving
4 + 9x + 2x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

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

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

Simplifying
x = -4
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 = {-4, -0.5}