(6x^3-29x^2)(37x-12)=0

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Solution for (6x^3-29x^2)(37x-12)=0 equation: 


Simplifying
(6x3 + -29x2)(37x + -12) = 0

Reorder the terms:
(-29x2 + 6x3)(37x + -12) = 0

Reorder the terms:
(-29x2 + 6x3)(-12 + 37x) = 0

Multiply (-29x2 + 6x3) * (-12 + 37x)
(-29x2 * (-12 + 37x) + 6x3 * (-12 + 37x)) = 0
((-12 * -29x2 + 37x * -29x2) + 6x3 * (-12 + 37x)) = 0
((348x2 + -1073x3) + 6x3 * (-12 + 37x)) = 0
(348x2 + -1073x3 + (-12 * 6x3 + 37x * 6x3)) = 0
(348x2 + -1073x3 + (-72x3 + 222x4)) = 0

Combine like terms: -1073x3 + -72x3 = -1145x3
(348x2 + -1145x3 + 222x4) = 0

Solving
348x2 + -1145x3 + 222x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(348 + -1145x + 222x2) = 0

Factor a trinomial.
x2((12 + -37x)(29 + -6x)) = 0


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 '(12 + -37x)' equal to zero and attempt to solve:

Simplifying
12 + -37x = 0

Solving
12 + -37x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -37x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -37x = 0 + -12
-37x = 0 + -12

Combine like terms: 0 + -12 = -12
-37x = -12

Divide each side by '-37'.
x = 0.3243243243

Simplifying
x = 0.3243243243

Subproblem 3
Set the factor '(29 + -6x)' equal to zero and attempt to solve:

Simplifying
29 + -6x = 0

Solving
29 + -6x = 0

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

Add '-29' to each side of the equation.
29 + -29 + -6x = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -6x = 0 + -29
-6x = 0 + -29

Combine like terms: 0 + -29 = -29
-6x = -29

Divide each side by '-6'.
x = 4.833333333

Simplifying
x = 4.833333333
Solution
x = {0, 0.3243243243, 4.833333333}

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