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

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

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

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

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

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

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

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

Solving for variable 'x'.

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {-0.5, 5}