4x(6x-7)(3x(2)+16)=

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Solution for 4x(6x-7)(3x(2)+16)= equation: 


Simplifying
4x(6x + -7)(3x(2) + 16) = 0

Reorder the terms:
4x(-7 + 6x)(3x(2) + 16) = 0

Reorder the terms for easier multiplication:
4x(-7 + 6x)(3 * 2x + 16) = 0

Multiply 3 * 2
4x(-7 + 6x)(6x + 16) = 0

Reorder the terms:
4x(-7 + 6x)(16 + 6x) = 0

Multiply (-7 + 6x) * (16 + 6x)
4x(-7(16 + 6x) + 6x * (16 + 6x)) = 0
4x((16 * -7 + 6x * -7) + 6x * (16 + 6x)) = 0
4x((-112 + -42x) + 6x * (16 + 6x)) = 0
4x(-112 + -42x + (16 * 6x + 6x * 6x)) = 0
4x(-112 + -42x + (96x + 36x2)) = 0

Combine like terms: -42x + 96x = 54x
4x(-112 + 54x + 36x2) = 0
(-112 * 4x + 54x * 4x + 36x2 * 4x) = 0
(-448x + 216x2 + 144x3) = 0

Solving
-448x + 216x2 + 144x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8x'.
8x(-56 + 27x + 18x2) = 0

Factor a trinomial.
8x((-8 + -3x)(7 + -6x)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
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 3
Set the factor '(7 + -6x)' equal to zero and attempt to solve:

Simplifying
7 + -6x = 0

Solving
7 + -6x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x = 0 + -7
-6x = 0 + -7

Combine like terms: 0 + -7 = -7
-6x = -7

Divide each side by '-6'.
x = 1.166666667

Simplifying
x = 1.166666667
Solution
x = {0, -2.666666667, 1.166666667}

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