(x-3)1+6=(x-3)(x+3)1

Solution for (x-3)1+6=(x-3)(x+3)1 equation:

Simplifying
(x + -3) * 1 + 6 = (x + -3)(x + 3) * 1

Reorder the terms:
(-3 + x) * 1 + 6 = (x + -3)(x + 3) * 1

Reorder the terms for easier multiplication:
1(-3 + x) + 6 = (x + -3)(x + 3) * 1
(-3 * 1 + x * 1) + 6 = (x + -3)(x + 3) * 1
(-3 + 1x) + 6 = (x + -3)(x + 3) * 1

Reorder the terms:
-3 + 6 + 1x = (x + -3)(x + 3) * 1

Combine like terms: -3 + 6 = 3
3 + 1x = (x + -3)(x + 3) * 1

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

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

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

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

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

Solving
3 + 1x = -9 + 1x2

Solving for variable 'x'.

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

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

Reorder the terms:
12 + 1x + -1x2 = -9 + 9 + 1x2 + -1x2

Combine like terms: -9 + 9 = 0
12 + 1x + -1x2 = 0 + 1x2 + -1x2
12 + 1x + -1x2 = 1x2 + -1x2

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

Factor a trinomial.
(4 + -1x)(3 + x) = 0

Subproblem 1
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
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 = {4, -3}