(5x-9)(6+x)=0

Solution for (5x-9)(6+x)=0 equation:

Simplifying
(5x + -9)(6 + x) = 0

Reorder the terms:
(-9 + 5x)(6 + x) = 0

Multiply (-9 + 5x) * (6 + x)
(-9(6 + x) + 5x * (6 + x)) = 0
((6 * -9 + x * -9) + 5x * (6 + x)) = 0
((-54 + -9x) + 5x * (6 + x)) = 0
(-54 + -9x + (6 * 5x + x * 5x)) = 0
(-54 + -9x + (30x + 5x2)) = 0

Combine like terms: -9x + 30x = 21x
(-54 + 21x + 5x2) = 0

Solving
-54 + 21x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -1x)(9 + -5x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

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

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

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(9 + -5x)' equal to zero and attempt to solve:

Simplifying
9 + -5x = 0

Solving
9 + -5x = 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 + -5x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5x = 0 + -9
-5x = 0 + -9

Combine like terms: 0 + -9 = -9
-5x = -9

Divide each side by '-5'.
x = 1.8

Simplifying
x = 1.8
Solution
x = {-6, 1.8}