(x+5)(2-3x)=0

Solution for (x+5)(2-3x)=0 equation:

Simplifying
(x + 5)(2 + -3x) = 0

Reorder the terms:
(5 + x)(2 + -3x) = 0

Multiply (5 + x) * (2 + -3x)
(5(2 + -3x) + x(2 + -3x)) = 0
((2 * 5 + -3x * 5) + x(2 + -3x)) = 0
((10 + -15x) + x(2 + -3x)) = 0
(10 + -15x + (2 * x + -3x * x)) = 0
(10 + -15x + (2x + -3x2)) = 0

Combine like terms: -15x + 2x = -13x
(10 + -13x + -3x2) = 0

Solving
10 + -13x + -3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -3x)(5 + x) = 0

Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

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

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

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

Simplifying
x = -5
Solution
x = {0.6666666667, -5}