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

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Solution for (-2x-5)(4x+1)=0 equation: 


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

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

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

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

Combine like terms: -20x + -2x = -22x
(-5 + -22x + -8x2) = 0

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

Solving for variable 'x'.

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

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

Ignore the factor -1.

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 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

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

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

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {-2.5, -0.25}

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