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

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Solution for 0=(x+2)(x-3) equation: 


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

Reorder the terms:
0 = (2 + x)(x + -3)

Reorder the terms:
0 = (2 + x)(-3 + x)

Multiply (2 + x) * (-3 + x)
0 = (2(-3 + x) + x(-3 + x))
0 = ((-3 * 2 + x * 2) + x(-3 + x))
0 = ((-6 + 2x) + x(-3 + x))
0 = (-6 + 2x + (-3 * x + x * x))
0 = (-6 + 2x + (-3x + x2))

Combine like terms: 2x + -3x = -1x
0 = (-6 + -1x + x2)

Solving
0 = -6 + -1x + x2

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(3 + -1x)(2 + x) = 0


Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3

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 = {3, -2}

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