(x+3)(2x+1)=3

Solution for (x+3)(2x+1)=3 equation:

Simplifying
(x + 3)(2x + 1) = 3

Reorder the terms:
(3 + x)(2x + 1) = 3

Reorder the terms:
(3 + x)(1 + 2x) = 3

Multiply (3 + x) * (1 + 2x)
(3(1 + 2x) + x(1 + 2x)) = 3
((1 * 3 + 2x * 3) + x(1 + 2x)) = 3
((3 + 6x) + x(1 + 2x)) = 3
(3 + 6x + (1 * x + 2x * x)) = 3
(3 + 6x + (1x + 2x2)) = 3

Combine like terms: 6x + 1x = 7x
(3 + 7x + 2x2) = 3

Add '-3' to each side of the equation.
3 + 7x + -3 + 2x2 = 3 + -3

Reorder the terms:
3 + -3 + 7x + 2x2 = 3 + -3

Combine like terms: 3 + -3 = 0
0 + 7x + 2x2 = 3 + -3
7x + 2x2 = 3 + -3

Combine like terms: 3 + -3 = 0
7x + 2x2 = 0

Solving
7x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + 2x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(7 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

Solving
7 + 2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5
Solution
x = {0, -3.5}