(3x-4)(9x+12x+16)=27(x^3)-64

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Solution for (3x-4)(9x+12x+16)=27(x^3)-64 equation: 


Simplifying
(3x + -4)(9x + 12x + 16) = 27(x3) + -64

Reorder the terms:
(-4 + 3x)(9x + 12x + 16) = 27(x3) + -64

Reorder the terms:
(-4 + 3x)(16 + 9x + 12x) = 27(x3) + -64

Combine like terms: 9x + 12x = 21x
(-4 + 3x)(16 + 21x) = 27(x3) + -64

Multiply (-4 + 3x) * (16 + 21x)
(-4(16 + 21x) + 3x * (16 + 21x)) = 27(x3) + -64
((16 * -4 + 21x * -4) + 3x * (16 + 21x)) = 27(x3) + -64
((-64 + -84x) + 3x * (16 + 21x)) = 27(x3) + -64
(-64 + -84x + (16 * 3x + 21x * 3x)) = 27(x3) + -64
(-64 + -84x + (48x + 63x2)) = 27(x3) + -64

Combine like terms: -84x + 48x = -36x
(-64 + -36x + 63x2) = 27(x3) + -64

Reorder the terms:
-64 + -36x + 63x2 = -64 + 27x3

Add '64' to each side of the equation.
-64 + -36x + 64 + 63x2 = -64 + 64 + 27x3

Reorder the terms:
-64 + 64 + -36x + 63x2 = -64 + 64 + 27x3

Combine like terms: -64 + 64 = 0
0 + -36x + 63x2 = -64 + 64 + 27x3
-36x + 63x2 = -64 + 64 + 27x3

Combine like terms: -64 + 64 = 0
-36x + 63x2 = 0 + 27x3
-36x + 63x2 = 27x3

Solving
-36x + 63x2 = 27x3

Solving for variable 'x'.

Combine like terms: 27x3 + -27x3 = 0
-36x + 63x2 + -27x3 = 0

Factor out the Greatest Common Factor (GCF), '9x'.
9x(-4 + 7x + -3x2) = 0

Factor a trinomial.
9x((-4 + 3x)(1 + -1x)) = 0

Ignore the factor 9.

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 '(-4 + 3x)' equal to zero and attempt to solve:

Simplifying
-4 + 3x = 0

Solving
-4 + 3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + 3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 3x = 0 + 4
3x = 0 + 4

Combine like terms: 0 + 4 = 4
3x = 4

Divide each side by '3'.
x = 1.333333333

Simplifying
x = 1.333333333

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {0, 1.333333333, 1}

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