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

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

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

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

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

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

Combine like terms: -5x + 2x = -3x
(-5 + -3x + 2x2) = 0

Solving
-5 + -3x + 2x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1
Subproblem 2
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
Solution
x = {-1, 2.5}