8x^3=22x^2-15x

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Solution for 8x^3=22x^2-15x equation: 


Simplifying
8x3 = 22x2 + -15x

Reorder the terms:
8x3 = -15x + 22x2

Solving
8x3 = -15x + 22x2

Solving for variable 'x'.

Reorder the terms:
15x + -22x2 + 8x3 = -15x + 22x2 + 15x + -22x2

Reorder the terms:
15x + -22x2 + 8x3 = -15x + 15x + 22x2 + -22x2

Combine like terms: -15x + 15x = 0
15x + -22x2 + 8x3 = 0 + 22x2 + -22x2
15x + -22x2 + 8x3 = 22x2 + -22x2

Combine like terms: 22x2 + -22x2 = 0
15x + -22x2 + 8x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(15 + -22x + 8x2) = 0

Factor a trinomial.
x((5 + -4x)(3 + -2x)) = 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 '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {0, 1.25, 1.5}

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