Solve by Factoring 4x^3-7x^2=3x^2

$4 x^{3} - 7 x^{2} = 3 x^{2}$

Subtract $3 x^{2}$ from both sides of the equation.

$4 x^{3} - 7 x^{2} - 3 x^{2} = 0$

Subtract $3 x^{2}$ from $- 7 x^{2}$ .

$4 x^{3} - 10 x^{2} = 0$

Factor $2 x^{2}$ out of $4 x^{3} - 10 x^{2}$ .

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

$2 x^{2} (2 x) - 10 x^{2} = 0$

Factor $2 x^{2}$ out of $- 10 x^{2}$ .

$2 x^{2} (2 x) + 2 x^{2} (- 5) = 0$

Factor $2 x^{2}$ out of $2 x^{2} (2 x) + 2 x^{2} (- 5)$ .

$2 x^{2} (2 x - 5) = 0$

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

$x^{2} = 0$

$2 x - 5 = 0$

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 square 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 $0$ .

$x = 0$

Set $2 x - 5$ equal to $0$ and solve for $x$ .

Set $2 x - 5$ equal to $0$ .

$2 x - 5 = 0$

Solve $2 x - 5 = 0$ for $x$ .

Add $5$ to both sides of the equation.

$2 x = 5$

Divide each term in $2 x = 5$ by $2$ and simplify.

Divide each term in $2 x = 5$ by $2$ .

$\frac{2 x}{2} = \frac{5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{5}{2}$

Divide $x$ by $1$ .

$x = \frac{5}{2}$

The final solution is all the values that make $2 x^{2} (2 x - 5) = 0$ true.

$x = 0, \frac{5}{2}$