4(8-3x)(8x+1)=0

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Solution for 4(8-3x)(8x+1)=0 equation: 


Simplifying
4(8 + -3x)(8x + 1) = 0

Reorder the terms:
4(8 + -3x)(1 + 8x) = 0

Multiply (8 + -3x) * (1 + 8x)
4(8(1 + 8x) + -3x * (1 + 8x)) = 0
4((1 * 8 + 8x * 8) + -3x * (1 + 8x)) = 0
4((8 + 64x) + -3x * (1 + 8x)) = 0
4(8 + 64x + (1 * -3x + 8x * -3x)) = 0
4(8 + 64x + (-3x + -24x2)) = 0

Combine like terms: 64x + -3x = 61x
4(8 + 61x + -24x2) = 0
(8 * 4 + 61x * 4 + -24x2 * 4) = 0
(32 + 244x + -96x2) = 0

Solving
32 + 244x + -96x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + 61x + -24x2) = 0

Factor a trinomial.
4((8 + -3x)(1 + 8x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 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 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667

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 = {2.666666667, -0.125}

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