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

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

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

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

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

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

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

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

Solving for variable 'x'.

Combine like terms: 0 + 15 = 15
15 + 7x + -2x2 = -15 + -7x + 2x2 + 15 + 7x + -2x2

Reorder the terms:
15 + 7x + -2x2 = -15 + 15 + -7x + 7x + 2x2 + -2x2

Combine like terms: -15 + 15 = 0
15 + 7x + -2x2 = 0 + -7x + 7x + 2x2 + -2x2
15 + 7x + -2x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
15 + 7x + -2x2 = 0 + 2x2 + -2x2
15 + 7x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
15 + 7x + -2x2 = 0

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}