Finite Math Examples

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

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Step 2

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

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Step 2.1

Add $2 x$ to both sides of the equation.

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

Step 2.2

Add $- x$ and $2 x$ .

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

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

Raise $x$ to the power of $1$ .

$x (4 x) + x = 0$

Step 3.3

Factor $x$ out of $x^{1}$ .

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

Step 3.4

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

Subtract $1$ from 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 6.2.2.3

Simplify the right side.

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Step 6.2.2.3.1

Move the negative in front of the fraction.

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

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:

$x = 0, - 0.25$