Finite Math Examples

$x = 80 x - 3 x^{2}$

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.

$80 x - 3 x^{2} = x$

Step 2

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

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Step 2.1

Subtract $x$ from both sides of the equation.

$80 x - 3 x^{2} - x = 0$

Step 2.2

Subtract $x$ from $80 x$ .

$- 3 x^{2} + 79 x = 0$

Step 3

Factor $- x$ out of $- 3 x^{2} + 79 x$ .

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Step 3.1

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

$- x (3 x) + 79 x = 0$

Step 3.2

Factor $- x$ out of $79 x$ .

$- x (3 x) - x \cdot - 79 = 0$

Step 3.3

Factor $- x$ out of $- x (3 x) - x (- 79)$ .

$- x (3 x - 79) = 0$

Step 4

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

$x = 0$

$3 x - 79 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $3 x - 79$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $3 x - 79$ equal to $0$ .

$3 x - 79 = 0$

Step 6.2

Solve $3 x - 79 = 0$ for $x$ .

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Step 6.2.1

Add $79$ to both sides of the equation.

$3 x = 79$

Step 6.2.2

Divide each term in $3 x = 79$ by $3$ and simplify.

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Step 6.2.2.1

Divide each term in $3 x = 79$ by $3$ .

$\frac{3 x}{3} = \frac{79}{3}$

Step 6.2.2.2

Simplify the left side.

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Step 6.2.2.2.1

Cancel the common factor of $3$ .

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Step 6.2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{79}{3}$

Step 6.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{79}{3}$

Step 7

The final solution is all the values that make $- x (3 x - 79) = 0$ true.

$x = 0, \frac{79}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = 0, \frac{79}{3}$

Decimal Form:

$x = 0, 26.\overline{3}$

Mixed Number Form:

$x = 0, 26 \frac{1}{3}$