Algebra Examples

$4 = 3 x^{2} + 14 x + 4$

Step 1

Rewrite the equation as $3 x^{2} + 14 x + 4 = 4$ .

$3 x^{2} + 14 x + 4 = 4$

Step 2

Subtract $4$ from both sides of the equation.

$3 x^{2} + 14 x + 4 - 4 = 0$

Step 3

Combine the opposite terms in $3 x^{2} + 14 x + 4 - 4$ .

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Step 3.1

Subtract $4$ from $4$ .

$3 x^{2} + 14 x + 0 = 0$

Step 3.2

Add $3 x^{2} + 14 x$ and $0$ .

$3 x^{2} + 14 x = 0$

Step 4

Factor $x$ out of $3 x^{2} + 14 x$ .

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Step 4.1

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

$x (3 x) + 14 x = 0$

Step 4.2

Factor $x$ out of $14 x$ .

$x (3 x) + x \cdot 14 = 0$

Step 4.3

Factor $x$ out of $x (3 x) + x \cdot 14$ .

$x (3 x + 14) = 0$

Step 5

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

$x = 0$

$3 x + 14 = 0$

Step 6

Set $x$ equal to $0$ .

$x = 0$

Step 7

Set $3 x + 14$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $3 x + 14$ equal to $0$ .

$3 x + 14 = 0$

Step 7.2

Solve $3 x + 14 = 0$ for $x$ .

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Step 7.2.1

Subtract $14$ from both sides of the equation.

$3 x = - 14$

Step 7.2.2

Divide each term in $3 x = - 14$ by $3$ and simplify.

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Step 7.2.2.1

Divide each term in $3 x = - 14$ by $3$ .

$\frac{3 x}{3} = \frac{- 14}{3}$

Step 7.2.2.2

Simplify the left side.

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Step 7.2.2.2.1

Cancel the common factor of $3$ .

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Step 7.2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 14}{3}$

Step 7.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 14}{3}$

Step 7.2.2.3

Simplify the right side.

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Step 7.2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{14}{3}$

Step 8

The final solution is all the values that make $x (3 x + 14) = 0$ true.

$x = 0, - \frac{14}{3}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$x = 0, - \frac{14}{3}$

Decimal Form:

$x = 0, - 4.\overline{6}$

Mixed Number Form:

$x = 0, - 4 \frac{2}{3}$