(6x+3)(9-x)=0

Solution for (6x+3)(9-x)=0 equation:

Simplifying
(6x + 3)(9 + -1x) = 0

Reorder the terms:
(3 + 6x)(9 + -1x) = 0

Multiply (3 + 6x) * (9 + -1x)
(3(9 + -1x) + 6x * (9 + -1x)) = 0
((9 * 3 + -1x * 3) + 6x * (9 + -1x)) = 0
((27 + -3x) + 6x * (9 + -1x)) = 0
(27 + -3x + (9 * 6x + -1x * 6x)) = 0
(27 + -3x + (54x + -6x2)) = 0

Combine like terms: -3x + 54x = 51x
(27 + 51x + -6x2) = 0

Solving
27 + 51x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 17x + -2x2) = 0

Factor a trinomial.
3((9 + -1x)(1 + 2x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

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

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

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {9, -0.5}