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

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

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

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

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

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

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

Solving
-15 + 7x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -1x)(3 + -2x) = 0

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
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
Solution
x = {-5, 1.5}