Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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

Step 4

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

$x^{2} = 0$

$2 x - 5 = 0$

Step 5

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

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Step 5.1

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

$x^{2} = 0$

Step 5.2

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

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Step 5.2.1

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

$x = \pm \sqrt{0}$

Step 5.2.2

Simplify $\pm \sqrt{0}$ .

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Step 5.2.2.1

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

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

Step 5.2.2.2

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

$x = \pm 0$

Step 5.2.2.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 6

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

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Step 6.1

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

$2 x - 5 = 0$

Step 6.2

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

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Step 6.2.1

Add $5$ to both sides of the equation.

$2 x = 5$

Step 6.2.2

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

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Step 6.2.2.1

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

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

Step 6.2.2.2

Simplify the left side.

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Step 6.2.2.2.1

Cancel the common factor of $2$ .

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Step 6.2.2.2.1.1

Cancel the common factor.

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

Step 6.2.2.2.1.2

Divide $x$ by $1$ .

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

Step 7

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

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