3x^2(4x-12)(4x-12)+x^3(2)(4x-12)(4)=0

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Solution for 3x^2(4x-12)(4x-12)+x^3(2)(4x-12)(4)=0 equation: 


Simplifying
3x2(4x + -12)(4x + -12) + x3(2)(4x + -12)(4) = 0

Reorder the terms:
3x2(-12 + 4x)(4x + -12) + x3(2)(4x + -12)(4) = 0

Reorder the terms:
3x2(-12 + 4x)(-12 + 4x) + x3(2)(4x + -12)(4) = 0

Multiply (-12 + 4x) * (-12 + 4x)
3x2(-12(-12 + 4x) + 4x * (-12 + 4x)) + x3(2)(4x + -12)(4) = 0
3x2((-12 * -12 + 4x * -12) + 4x * (-12 + 4x)) + x3(2)(4x + -12)(4) = 0
3x2((144 + -48x) + 4x * (-12 + 4x)) + x3(2)(4x + -12)(4) = 0
3x2(144 + -48x + (-12 * 4x + 4x * 4x)) + x3(2)(4x + -12)(4) = 0
3x2(144 + -48x + (-48x + 16x2)) + x3(2)(4x + -12)(4) = 0

Combine like terms: -48x + -48x = -96x
3x2(144 + -96x + 16x2) + x3(2)(4x + -12)(4) = 0
(144 * 3x2 + -96x * 3x2 + 16x2 * 3x2) + x3(2)(4x + -12)(4) = 0
(432x2 + -288x3 + 48x4) + x3(2)(4x + -12)(4) = 0

Reorder the terms:
432x2 + -288x3 + 48x4 + x3 * 2(-12 + 4x)(4) = 0

Reorder the terms for easier multiplication:
432x2 + -288x3 + 48x4 + 2 * 4x3(-12 + 4x) = 0

Multiply 2 * 4
432x2 + -288x3 + 48x4 + 8x3(-12 + 4x) = 0
432x2 + -288x3 + 48x4 + (-12 * 8x3 + 4x * 8x3) = 0
432x2 + -288x3 + 48x4 + (-96x3 + 32x4) = 0

Reorder the terms:
432x2 + -288x3 + -96x3 + 48x4 + 32x4 = 0

Combine like terms: -288x3 + -96x3 = -384x3
432x2 + -384x3 + 48x4 + 32x4 = 0

Combine like terms: 48x4 + 32x4 = 80x4
432x2 + -384x3 + 80x4 = 0

Solving
432x2 + -384x3 + 80x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '16x2'.
16x2(27 + -24x + 5x2) = 0

Factor a trinomial.
16x2((9 + -5x)(3 + -1x)) = 0

Ignore the factor 16.

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 '(9 + -5x)' equal to zero and attempt to solve:

Simplifying
9 + -5x = 0

Solving
9 + -5x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -5x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5x = 0 + -9
-5x = 0 + -9

Combine like terms: 0 + -9 = -9
-5x = -9

Divide each side by '-5'.
x = 1.8

Simplifying
x = 1.8

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, 1.8, 3}

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