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

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


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

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

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

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

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

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

Multiply (-3 + x) * (3 + x)
1 + 3x = (-3(3 + x) + x(3 + x))
1 + 3x = ((3 * -3 + x * -3) + x(3 + x))
1 + 3x = ((-9 + -3x) + x(3 + x))
1 + 3x = (-9 + -3x + (3 * x + x * x))
1 + 3x = (-9 + -3x + (3x + x2))

Combine like terms: -3x + 3x = 0
1 + 3x = (-9 + 0 + x2)
1 + 3x = (-9 + x2)

Solving
1 + 3x = -9 + x2

Solving for variable 'x'.

Reorder the terms:
1 + 9 + 3x + -1x2 = -9 + x2 + 9 + -1x2

Combine like terms: 1 + 9 = 10
10 + 3x + -1x2 = -9 + x2 + 9 + -1x2

Reorder the terms:
10 + 3x + -1x2 = -9 + 9 + x2 + -1x2

Combine like terms: -9 + 9 = 0
10 + 3x + -1x2 = 0 + x2 + -1x2
10 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10 + 3x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(2 + x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2
Solution
x = {5, -2}

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