(8x+1)(-4x-8)=0

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Solution for (8x+1)(-4x-8)=0 equation: 


Simplifying
(8x + 1)(-4x + -8) = 0

Reorder the terms:
(1 + 8x)(-4x + -8) = 0

Reorder the terms:
(1 + 8x)(-8 + -4x) = 0

Multiply (1 + 8x) * (-8 + -4x)
(1(-8 + -4x) + 8x * (-8 + -4x)) = 0
((-8 * 1 + -4x * 1) + 8x * (-8 + -4x)) = 0
((-8 + -4x) + 8x * (-8 + -4x)) = 0
(-8 + -4x + (-8 * 8x + -4x * 8x)) = 0
(-8 + -4x + (-64x + -32x2)) = 0

Combine like terms: -4x + -64x = -68x
(-8 + -68x + -32x2) = 0

Solving
-8 + -68x + -32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-4'.
-4(2 + 17x + 8x2) = 0

Factor a trinomial.
-4((2 + x)(1 + 8x)) = 0

Ignore the factor -4.

Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2

Subproblem 2
Set the factor '(1 + 8x)' equal to zero and attempt to solve:

Simplifying
1 + 8x = 0

Solving
1 + 8x = 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 + 8x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 8x = 0 + -1
8x = 0 + -1

Combine like terms: 0 + -1 = -1
8x = -1

Divide each side by '8'.
x = -0.125

Simplifying
x = -0.125
Solution
x = {-2, -0.125}

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