Examples

$3 x^{2} - x (3 - x) = 0$

Step 1

Simplify $3 x^{2} - x (3 - x)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 x^{2} - x \cdot 3 - x (- x) = 0$

Step 1.1.2

Multiply $3$ by $- 1$ .

$3 x^{2} - 3 x - x (- x) = 0$

Step 1.1.3

Rewrite using the commutative property of multiplication.

$3 x^{2} - 3 x - 1 \cdot - 1 x \cdot x = 0$

Step 1.1.4

Simplify each term.

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Step 1.1.4.1

Multiply $x$ by $x$ by adding the exponents.

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Step 1.1.4.1.1

Move $x$ .

$3 x^{2} - 3 x - 1 \cdot - 1 (x \cdot x) = 0$

Step 1.1.4.1.2

Multiply $x$ by $x$ .

$3 x^{2} - 3 x - 1 \cdot - 1 x^{2} = 0$

Step 1.1.4.2

Multiply $- 1$ by $- 1$ .

$3 x^{2} - 3 x + 1 x^{2} = 0$

Step 1.1.4.3

Multiply $x^{2}$ by $1$ .

$3 x^{2} - 3 x + x^{2} = 0$

Step 1.2

Add $3 x^{2}$ and $x^{2}$ .

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

Step 2

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

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Step 2.1

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

$x (4 x) - 3 x = 0$

Step 2.2

Factor $x$ out of $- 3 x$ .

$x (4 x) + x \cdot - 3 = 0$

Step 2.3

Factor $x$ out of $x (4 x) + x \cdot - 3$ .

$x (4 x - 3) = 0$

Step 3

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

$x = 0$

$4 x - 3 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

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

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Step 5.1

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

$4 x - 3 = 0$

Step 5.2

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

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Step 5.2.1

Add $3$ to both sides of the equation.

$4 x = 3$

Step 5.2.2

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

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Step 5.2.2.1

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

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

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.

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

Step 5.2.2.2.1.2

Divide $x$ by $1$ .

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

Step 6

The final solution is all the values that make $x (4 x - 3) = 0$ true.

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

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