6x^2(12x^2+13x-55)=0

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Solution for 6x^2(12x^2+13x-55)=0 equation: 


Simplifying
6x2(12x2 + 13x + -55) = 0

Reorder the terms:
6x2(-55 + 13x + 12x2) = 0
(-55 * 6x2 + 13x * 6x2 + 12x2 * 6x2) = 0
(-330x2 + 78x3 + 72x4) = 0

Solving
-330x2 + 78x3 + 72x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x2'.
6x2(-55 + 13x + 12x2) = 0

Factor a trinomial.
6x2((-11 + -4x)(5 + -3x)) = 0

Ignore the factor 6.

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 '(-11 + -4x)' equal to zero and attempt to solve:

Simplifying
-11 + -4x = 0

Solving
-11 + -4x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -4x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -4x = 0 + 11
-4x = 0 + 11

Combine like terms: 0 + 11 = 11
-4x = 11

Divide each side by '-4'.
x = -2.75

Simplifying
x = -2.75

Subproblem 3
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {0, -2.75, 1.666666667}

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