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

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


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

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

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

Combine like terms: -2x + 20x = 18x
(8 + 18x + -5x2) = 0

Solving
8 + 18x + -5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x)(2 + 5x) = 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 '(2 + 5x)' equal to zero and attempt to solve:

Simplifying
2 + 5x = 0

Solving
2 + 5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5x = 0 + -2

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

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

Divide each side by '5'.
x = -0.4

Simplifying
x = -0.4
Solution
x = {4, -0.4}

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