0=(x-5)(2x+1)

Solution for 0=(x-5)(2x+1) equation:

Simplifying
0 = (x + -5)(2x + 1)

Reorder the terms:
0 = (-5 + x)(2x + 1)

Reorder the terms:
0 = (-5 + x)(1 + 2x)

Multiply (-5 + x) * (1 + 2x)
0 = (-5(1 + 2x) + x(1 + 2x))
0 = ((1 * -5 + 2x * -5) + x(1 + 2x))
0 = ((-5 + -10x) + x(1 + 2x))
0 = (-5 + -10x + (1 * x + 2x * x))
0 = (-5 + -10x + (1x + 2x2))

Combine like terms: -10x + 1x = -9x
0 = (-5 + -9x + 2x2)

Solving
0 = -5 + -9x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 5 = 5
5 + 9x + -2x2 = -5 + -9x + 2x2 + 5 + 9x + -2x2

Reorder the terms:
5 + 9x + -2x2 = -5 + 5 + -9x + 9x + 2x2 + -2x2

Combine like terms: -5 + 5 = 0
5 + 9x + -2x2 = 0 + -9x + 9x + 2x2 + -2x2
5 + 9x + -2x2 = -9x + 9x + 2x2 + -2x2

Combine like terms: -9x + 9x = 0
5 + 9x + -2x2 = 0 + 2x2 + -2x2
5 + 9x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5 + 9x + -2x2 = 0

Factor a trinomial.
(5 + -1x)(1 + 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 '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {5, -0.5}