Precalculus Examples

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

Step 1

Add $3$ to both sides of the equation.

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

Step 2

Combine the opposite terms in $4 x^{2} - x - 3 + 3$ .

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Step 2.1

Add $- 3$ and $3$ .

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

Step 2.2

Add $4 x^{2} - x$ and $0$ .

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

Step 3

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

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Step 3.1

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

$x (4 x) - x = 0$

Step 3.2

Factor $x$ out of $- x$ .

$x (4 x) + x \cdot - 1 = 0$

Step 3.3

Factor $x$ out of $x (4 x) + x \cdot - 1$ .

$x (4 x - 1) = 0$

Step 4

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

$x = 0$

$4 x - 1 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $4 x - 1$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $4 x - 1$ equal to $0$ .

$4 x - 1 = 0$

Step 6.2

Solve $4 x - 1 = 0$ for $x$ .

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Step 6.2.1

Add $1$ to both sides of the equation.

$4 x = 1$

Step 6.2.2

Divide each term in $4 x = 1$ by $4$ and simplify.

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Step 6.2.2.1

Divide each term in $4 x = 1$ by $4$ .

$\frac{4 x}{4} = \frac{1}{4}$

Step 6.2.2.2

Simplify the left side.

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Step 6.2.2.2.1

Cancel the common factor of $4$ .

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Step 6.2.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{1}{4}$

Step 6.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{4}$

Step 7

The final solution is all the values that make $x (4 x - 1) = 0$ true.

$x = 0, \frac{1}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = 0, \frac{1}{4}$

Decimal Form:

$x = 0, 0.25$