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

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

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

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

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

Multiply (-5 + 2x) * (3 + x)
0 = (-5(3 + x) + 2x * (3 + x))
0 = ((3 * -5 + x * -5) + 2x * (3 + x))
0 = ((-15 + -5x) + 2x * (3 + x))
0 = (-15 + -5x + (3 * 2x + x * 2x))
0 = (-15 + -5x + (6x + 2x2))

Combine like terms: -5x + 6x = 1x
0 = (-15 + 1x + 2x2)

Solving
0 = -15 + 1x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 15 = 15
15 + -1x + -2x2 = -15 + 1x + 2x2 + 15 + -1x + -2x2

Reorder the terms:
15 + -1x + -2x2 = -15 + 15 + 1x + -1x + 2x2 + -2x2

Combine like terms: -15 + 15 = 0
15 + -1x + -2x2 = 0 + 1x + -1x + 2x2 + -2x2
15 + -1x + -2x2 = 1x + -1x + 2x2 + -2x2

Combine like terms: 1x + -1x = 0
15 + -1x + -2x2 = 0 + 2x2 + -2x2
15 + -1x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
15 + -1x + -2x2 = 0

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

Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {2.5, -3}