3x^2(x-6)(x+8)=0

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Solution for 3x^2(x-6)(x+8)=0 equation: 


Simplifying
3x2(x + -6)(x + 8) = 0

Reorder the terms:
3x2(-6 + x)(x + 8) = 0

Reorder the terms:
3x2(-6 + x)(8 + x) = 0

Multiply (-6 + x) * (8 + x)
3x2(-6(8 + x) + x(8 + x)) = 0
3x2((8 * -6 + x * -6) + x(8 + x)) = 0
3x2((-48 + -6x) + x(8 + x)) = 0
3x2(-48 + -6x + (8 * x + x * x)) = 0
3x2(-48 + -6x + (8x + x2)) = 0

Combine like terms: -6x + 8x = 2x
3x2(-48 + 2x + x2) = 0
(-48 * 3x2 + 2x * 3x2 + x2 * 3x2) = 0
(-144x2 + 6x3 + 3x4) = 0

Solving
-144x2 + 6x3 + 3x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(-48 + 2x + x2) = 0

Factor a trinomial.
3x2((-8 + -1x)(6 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

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

Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, -8, 6}

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