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

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


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

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

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

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

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

Solving
0 = -8 + -31x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 8 = 8
8 + 31x + -4x2 = -8 + -31x + 4x2 + 8 + 31x + -4x2

Reorder the terms:
8 + 31x + -4x2 = -8 + 8 + -31x + 31x + 4x2 + -4x2

Combine like terms: -8 + 8 = 0
8 + 31x + -4x2 = 0 + -31x + 31x + 4x2 + -4x2
8 + 31x + -4x2 = -31x + 31x + 4x2 + -4x2

Combine like terms: -31x + 31x = 0
8 + 31x + -4x2 = 0 + 4x2 + -4x2
8 + 31x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
8 + 31x + -4x2 = 0

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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