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

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


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

Reorder the terms:
(2 + 5x)(-1x + -4) = 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 = -22x
(-8 + -22x + -5x2) = 0

Solving
-8 + -22x + -5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 22x + 5x2) = 0

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

Ignore the factor -1.

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

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

Combine like terms: 0 + -4 = -4
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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