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

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


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

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

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

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

Combine like terms: -24x + 1x = -23x
4(-8 + -23x + 3x2) = 0
(-8 * 4 + -23x * 4 + 3x2 * 4) = 0
(-32 + -92x + 12x2) = 0

Solving
-32 + -92x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-8 + -23x + 3x2) = 0

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

Ignore the factor 4.

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

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
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
Solution
x = {-0.3333333333, 8}

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