6x^4=33x^3-42x^2

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Solution for 6x^4=33x^3-42x^2 equation: 


Simplifying
6x4 = 33x3 + -42x2

Reorder the terms:
6x4 = -42x2 + 33x3

Solving
6x4 = -42x2 + 33x3

Solving for variable 'x'.

Reorder the terms:
42x2 + -33x3 + 6x4 = -42x2 + 33x3 + 42x2 + -33x3

Reorder the terms:
42x2 + -33x3 + 6x4 = -42x2 + 42x2 + 33x3 + -33x3

Combine like terms: -42x2 + 42x2 = 0
42x2 + -33x3 + 6x4 = 0 + 33x3 + -33x3
42x2 + -33x3 + 6x4 = 33x3 + -33x3

Combine like terms: 33x3 + -33x3 = 0
42x2 + -33x3 + 6x4 = 0

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(14 + -11x + 2x2) = 0

Factor a trinomial.
3x2((2 + -1x)(7 + -2x)) = 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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 3
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {0, 2, 3.5}

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