Solve by Factoring 4x^3=9x^2

$4 x^{3} = 9 x^{2}$

Step 1

Subtract $9 x^{2}$ from both sides of the equation.

$4 x^{3} - 9 x^{2} = 0$

Step 2

Factor $x^{2}$ out of $4 x^{3} - 9 x^{2}$ .

Factor $x^{2}$ out of $4 x^{3}$ .

$x^{2} (4 x) - 9 x^{2} = 0$

Factor $x^{2}$ out of $- 9 x^{2}$ .

$x^{2} (4 x) + x^{2} \cdot - 9 = 0$

Factor $x^{2}$ out of $x^{2} (4 x) + x^{2} \cdot - 9$ .

$x^{2} (4 x - 9) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x^{2} = 0$

$4 x - 9 = 0$

Step 4

Set $x^{2}$ equal to $0$ and solve for $x$ .

Set $x^{2}$ equal to $0$ .

$x^{2} = 0$

Solve $x^{2} = 0$ for $x$ .

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

Step 5

Set $4 x - 9$ equal to $0$ and solve for $x$ .

Set $4 x - 9$ equal to $0$ .

$4 x - 9 = 0$

Solve $4 x - 9 = 0$ for $x$ .

Add $9$ to both sides of the equation.

$4 x = 9$

Divide each term in $4 x = 9$ by $4$ and simplify.

Divide each term in $4 x = 9$ by $4$ .

$\frac{4 x}{4} = \frac{9}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{9}{4}$

Divide $x$ by $1$ .

$x = \frac{9}{4}$

Step 6

The final solution is all the values that make $x^{2} (4 x - 9) = 0$ true.

$x = 0, \frac{9}{4}$

Solve by Factoring 4x^3=9x^2

Related Questions

Support LCMGCF.com by disabling your adblocker.