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

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


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

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

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

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

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

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

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

Multiply (2 + x) * (-3 + x)
3 + 5x + 2x2 = (2(-3 + x) + x(-3 + x))
3 + 5x + 2x2 = ((-3 * 2 + x * 2) + x(-3 + x))
3 + 5x + 2x2 = ((-6 + 2x) + x(-3 + x))
3 + 5x + 2x2 = (-6 + 2x + (-3 * x + x * x))
3 + 5x + 2x2 = (-6 + 2x + (-3x + x2))

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

Solving
3 + 5x + 2x2 = -6 + -1x + x2

Solving for variable 'x'.

Reorder the terms:
3 + 6 + 5x + x + 2x2 + -1x2 = -6 + -1x + x2 + 6 + x + -1x2

Combine like terms: 3 + 6 = 9
9 + 5x + x + 2x2 + -1x2 = -6 + -1x + x2 + 6 + x + -1x2

Combine like terms: 5x + x = 6x
9 + 6x + 2x2 + -1x2 = -6 + -1x + x2 + 6 + x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
9 + 6x + 1x2 = -6 + -1x + x2 + 6 + x + -1x2

Reorder the terms:
9 + 6x + 1x2 = -6 + 6 + -1x + x + x2 + -1x2

Combine like terms: -6 + 6 = 0
9 + 6x + 1x2 = 0 + -1x + x + x2 + -1x2
9 + 6x + 1x2 = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
9 + 6x + 1x2 = 0 + x2 + -1x2
9 + 6x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
9 + 6x + 1x2 = 0

Factor a trinomial.
(3 + x)(3 + x) = 0


Subproblem 1
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

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 = {-3, -3}

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