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

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


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

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

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

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

Combine like terms: 32x + -1x = 31x
(-8 + 31x + 4x2) = 0

Solving
-8 + 31x + 4x2 = 0

Solving for variable 'x'.

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


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

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

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

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

Divide each side by '-1'.
x = -8

Simplifying
x = -8

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 = {-8, 0.25}

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