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

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

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

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

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

Combine like terms: 3x + -10x = -7x
(15 + -7x + -2x2) = 0

Solving
15 + -7x + -2x2 = 0

Solving for variable 'x'.

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

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
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 = {1.5, -5}