(3x-5)(x+6)=0

Solution for (3x-5)(x+6)=0 equation:

Simplifying
(3x + -5)(x + 6) = 0

Reorder the terms:
(-5 + 3x)(x + 6) = 0

Reorder the terms:
(-5 + 3x)(6 + x) = 0

Multiply (-5 + 3x) * (6 + x)
(-5(6 + x) + 3x * (6 + x)) = 0
((6 * -5 + x * -5) + 3x * (6 + x)) = 0
((-30 + -5x) + 3x * (6 + x)) = 0
(-30 + -5x + (6 * 3x + x * 3x)) = 0
(-30 + -5x + (18x + 3x2)) = 0

Combine like terms: -5x + 18x = 13x
(-30 + 13x + 3x2) = 0

Solving
-30 + 13x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -1x)(5 + -3x) = 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 '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-6, 1.666666667}