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

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

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

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

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

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

Solving
5 + 3x + -2x2 = 0

Solving for variable 'x'.

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

Simplifying
1 + x = 0

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

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

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

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