9((-3-x)(1-x))=0

Solution for 9((-3-x)(1-x))=0 equation:

Simplifying
9((-3 + -1x)(1 + -1x)) = 0

Multiply (-3 + -1x) * (1 + -1x)
9((-3(1 + -1x) + -1x * (1 + -1x))) = 0
9(((1 * -3 + -1x * -3) + -1x * (1 + -1x))) = 0
9(((-3 + 3x) + -1x * (1 + -1x))) = 0
9((-3 + 3x + (1 * -1x + -1x * -1x))) = 0
9((-3 + 3x + (-1x + 1x2))) = 0

Combine like terms: 3x + -1x = 2x
9((-3 + 2x + 1x2)) = 0
(-3 * 9 + 2x * 9 + 1x2 * 9) = 0
(-27 + 18x + 9x2) = 0

Solving
-27 + 18x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-3 + 2x + x2) = 0

Factor a trinomial.
9((-3 + -1x)(1 + -1x)) = 0

Ignore the factor 9.
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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-3, 1}