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

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

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

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

Remove parenthesis around (3 + x)
3 + x = (2x + -1)(x + 3)

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

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

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

Combine like terms: -1x + 6x = 5x
3 + x = (-3 + 5x + 2x2)

Solving
3 + x = -3 + 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
3 + 3 + x + -5x + -2x2 = -3 + 5x + 2x2 + 3 + -5x + -2x2

Combine like terms: 3 + 3 = 6
6 + x + -5x + -2x2 = -3 + 5x + 2x2 + 3 + -5x + -2x2

Combine like terms: x + -5x = -4x
6 + -4x + -2x2 = -3 + 5x + 2x2 + 3 + -5x + -2x2

Reorder the terms:
6 + -4x + -2x2 = -3 + 3 + 5x + -5x + 2x2 + -2x2

Combine like terms: -3 + 3 = 0
6 + -4x + -2x2 = 0 + 5x + -5x + 2x2 + -2x2
6 + -4x + -2x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
6 + -4x + -2x2 = 0 + 2x2 + -2x2
6 + -4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
6 + -4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -2x + -1x2) = 0

Factor a trinomial.
2((1 + -1x)(3 + x)) = 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {1, -3}