Algebra Examples

$4 a^{3} - a^{2} = 2 a^{2}$

Step 1

Move all terms containing $a$ to the left side of the equation.

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Step 1.1

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

$4 a^{3} - a^{2} - 2 a^{2} = 0$

Step 1.2

Subtract $2 a^{2}$ from $- a^{2}$ .

$4 a^{3} - 3 a^{2} = 0$

Step 2

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

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Step 2.1

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

$a^{2} (4 a) - 3 a^{2} = 0$

Step 2.2

Factor $a^{2}$ out of $- 3 a^{2}$ .

$a^{2} (4 a) + a^{2} \cdot - 3 = 0$

Step 2.3

Factor $a^{2}$ out of $a^{2} (4 a) + a^{2} \cdot - 3$ .

$a^{2} (4 a - 3) = 0$

Step 3

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

$a^{2} = 0$

$4 a - 3 = 0$

Step 4

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

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Step 4.1

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

$a^{2} = 0$

Step 4.2

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

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Step 4.2.1

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

$a = \pm \sqrt{0}$

Step 4.2.2

Simplify $\pm \sqrt{0}$ .

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Step 4.2.2.1

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

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

Step 4.2.2.2

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

$a = \pm 0$

Step 4.2.2.3

Plus or minus $0$ is $0$ .

$a = 0$

Step 5

Set $4 a - 3$ equal to $0$ and solve for $a$ .

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Step 5.1

Set $4 a - 3$ equal to $0$ .

$4 a - 3 = 0$

Step 5.2

Solve $4 a - 3 = 0$ for $a$ .

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Step 5.2.1

Add $3$ to both sides of the equation.

$4 a = 3$

Step 5.2.2

Divide each term in $4 a = 3$ by $4$ and simplify.

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Step 5.2.2.1

Divide each term in $4 a = 3$ by $4$ .

$\frac{4 a}{4} = \frac{3}{4}$

Step 5.2.2.2

Simplify the left side.

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Step 5.2.2.2.1

Cancel the common factor of $4$ .

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Step 5.2.2.2.1.1

Cancel the common factor.

$\frac{4 a}{4} = \frac{3}{4}$

Step 5.2.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{3}{4}$

Step 6

The final solution is all the values that make $a^{2} (4 a - 3) = 0$ true.

$a = 0, \frac{3}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$a = 0, \frac{3}{4}$

Decimal Form:

$a = 0, 0.75$