solve for x: 2x^3 + 9x^2= 5x?

Question

thank you!

Answer 1

2x^3 + 9x^2= 5x?

2x^3 + 9x^2 -5x = 0
Factor out an X

x( 2x^2 + 9x -5)=0
Factor
X(2x-1)(x+5)=0

X= -5
X= 1/2
X= 0

...I didn't bother plugging them in to see if there were any Extraneous Roots (False Roots) but you can check that with a calculator...

Answer 2

Simplifying
2x^3 + 9x^2 = 5x

Reorder the terms:
9x^2 + 2x^3 = 5x

Solving
9x^2 + 2x^3 = 5x

Solving for variable 'x'.

Reorder the terms:
-5x + 9x^2 + 2x^3 = 5x + -5x

Combine like terms: 5x + -5x = 0
-5x + 9x^2 + 2x^3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + 9x + 2x2) = 0

Factor a trinomial.
x((-5 + -1x)(1 + -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 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 3
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0, -5, 0.5}

Answer 3

2x^3+9x^2-5x=0

x(2x^2+9x-5)=0

(2x-1)(x+5)=0

x=0 1/2 -5

Answer 4

11x^2 = 5x
11x^2 - 5x = 0
x(11x - 5) = 0
x = 0
11x - 5 = 0
11x = 5
x = 5/11

(0, 5/11)

Answer 5

can be rewritten as
x(2x^2+9x-5)=0
x(2x^2+10x-x-5)=0
x(2x(x+5)-1(x+1))=0
x(2x-1)(x+1)=0
x=0,0.5,-1