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

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

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

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

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

Multiply (6 + 5x) * (-9 + x)
0 = (6(-9 + x) + 5x * (-9 + x))
0 = ((-9 * 6 + x * 6) + 5x * (-9 + x))
0 = ((-54 + 6x) + 5x * (-9 + x))
0 = (-54 + 6x + (-9 * 5x + x * 5x))
0 = (-54 + 6x + (-45x + 5x2))

Combine like terms: 6x + -45x = -39x
0 = (-54 + -39x + 5x2)

Solving
0 = -54 + -39x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + 54 = 54
54 + 39x + -5x2 = -54 + -39x + 5x2 + 54 + 39x + -5x2

Reorder the terms:
54 + 39x + -5x2 = -54 + 54 + -39x + 39x + 5x2 + -5x2

Combine like terms: -54 + 54 = 0
54 + 39x + -5x2 = 0 + -39x + 39x + 5x2 + -5x2
54 + 39x + -5x2 = -39x + 39x + 5x2 + -5x2

Combine like terms: -39x + 39x = 0
54 + 39x + -5x2 = 0 + 5x2 + -5x2
54 + 39x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
54 + 39x + -5x2 = 0

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

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 '(6 + 5x)' equal to zero and attempt to solve:

Simplifying
6 + 5x = 0

Solving
6 + 5x = 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 + 5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5x = 0 + -6
5x = 0 + -6

Combine like terms: 0 + -6 = -6
5x = -6

Divide each side by '5'.
x = -1.2

Simplifying
x = -1.2
Solution
x = {9, -1.2}