(x+3)(x-3)-x=3

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


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

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

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

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

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

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

Solving
-9 + -1x + x2 = 3

Solving for variable 'x'.

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

Combine like terms: -9 + -3 = -12
-12 + -1x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-12 + -1x + x2 = 0

Factor a trinomial.
(-3 + -1x)(4 + -1x) = 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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-3, 4}

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