(2x+5)(4-x)=0

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Solution for (2x+5)(4-x)=0 equation: 


Simplifying
(2x + 5)(4 + -1x) = 0

Reorder the terms:
(5 + 2x)(4 + -1x) = 0

Multiply (5 + 2x) * (4 + -1x)
(5(4 + -1x) + 2x * (4 + -1x)) = 0
((4 * 5 + -1x * 5) + 2x * (4 + -1x)) = 0
((20 + -5x) + 2x * (4 + -1x)) = 0
(20 + -5x + (4 * 2x + -1x * 2x)) = 0
(20 + -5x + (8x + -2x2)) = 0

Combine like terms: -5x + 8x = 3x
(20 + 3x + -2x2) = 0

Solving
20 + 3x + -2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x)(5 + 2x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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 = {4, -2.5}

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