x^2(3x-5)=22x

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Solution for x^2(3x-5)=22x equation: 


Simplifying
x2(3x + -5) = 22x

Reorder the terms:
x2(-5 + 3x) = 22x
(-5 * x2 + 3x * x2) = 22x
(-5x2 + 3x3) = 22x

Solving
-5x2 + 3x3 = 22x

Solving for variable 'x'.

Reorder the terms:
-22x + -5x2 + 3x3 = 22x + -22x

Combine like terms: 22x + -22x = 0
-22x + -5x2 + 3x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-22 + -5x + 3x2) = 0

Factor a trinomial.
x((-2 + -1x)(11 + -3x)) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
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 '(11 + -3x)' equal to zero and attempt to solve:

Simplifying
11 + -3x = 0

Solving
11 + -3x = 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 + -3x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3x = 0 + -11
-3x = 0 + -11

Combine like terms: 0 + -11 = -11
-3x = -11

Divide each side by '-3'.
x = 3.666666667

Simplifying
x = 3.666666667
Solution
x = {0, -2, 3.666666667}

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