Algebra Examples

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

Factor the $e q u a t i o n$ .

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

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

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

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

Move $x$ .

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

Multiply $3$ by $x$ .

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

Move $x$ .

$x (3 x) + x (- 1 (3 - x)) = 0$

Factor $x$ out of $x (3 x) + x (- 1 (3 - x))$ .

$x (3 x - 1 (3 - x)) = 0$

Rewrite $- 1 (3 - x)$ as $- (3 - x)$ .

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

Simplify inside each of the factors.

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Simplify each term.

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Apply the distributive property.

$x (3 x + (- 1 \cdot 3 + x)) = 0$

Multiply $- 1$ by $3$ .

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

Simplify $- - x$ .

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Multiply $- 1$ by $- 1$ .

$x (3 x + (- 3 + 1 x)) = 0$

Multiply $x$ by $1$ .

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

Simplify by adding terms.

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Remove unnecessary parentheses.

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

Add $3 x$ and $x$ .

$x (4 x - 3) = 0$

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

$x = 0$

$4 x - 3 = 0$

Set the first factor equal to $0$ .

$x = 0$

Set the next factor equal to $0$ and solve.

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Set the next factor equal to $0$ .

$4 x - 3 = 0$

Add $3$ to both sides of the equation.

$4 x = 3$

Divide each term by $4$ and simplify.

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

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

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

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

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

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