Algebra Examples

$N = \frac{t^{2} - t}{2}$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Simplify the right side.

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Step 1.1.1

Factor $t$ out of $t^{2} - t$ .

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Step 1.1.1.1

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

$N = \frac{t \cdot t - t}{2}$

Step 1.1.1.2

Factor $t$ out of $- t$ .

$N = \frac{t \cdot t + t \cdot - 1}{2}$

Step 1.1.1.3

Factor $t$ out of $t \cdot t + t \cdot - 1$ .

$N = \frac{t (t - 1)}{2}$

Step 1.2

Subtract $\frac{t (t - 1)}{2}$ from both sides of the equation.

$N - \frac{t (t - 1)}{2} = 0$

Step 2

Simplify $N - \frac{t (t - 1)}{2}$ .

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Step 2.1

To write $N$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$N \cdot \frac{2}{2} - \frac{t (t - 1)}{2} = 0$

Step 2.2

Simplify terms.

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Step 2.2.1

Combine $N$ and $\frac{2}{2}$ .

$\frac{N \cdot 2}{2} - \frac{t (t - 1)}{2} = 0$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{N \cdot 2 - t (t - 1)}{2} = 0$

Step 2.3

Simplify the numerator.

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Step 2.3.1

Move $2$ to the left of $N$ .

$\frac{2 \cdot N - t (t - 1)}{2} = 0$

Step 2.3.2

Apply the distributive property.

$\frac{2 N - t \cdot t - t \cdot - 1}{2} = 0$

Step 2.3.3

Multiply $t$ by $t$ by adding the exponents.

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Step 2.3.3.1

Move $t$ .

$\frac{2 N - (t \cdot t) - t \cdot - 1}{2} = 0$

Step 2.3.3.2

Multiply $t$ by $t$ .

$\frac{2 N - t^{2} - t \cdot - 1}{2} = 0$

Step 2.3.4

Multiply $- t \cdot - 1$ .

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Step 2.3.4.1

Multiply $- 1$ by $- 1$ .

$\frac{2 N - t^{2} + 1 t}{2} = 0$

Step 2.3.4.2

Multiply $t$ by $1$ .

$\frac{2 N - t^{2} + t}{2} = 0$

Step 3

Set the numerator equal to zero.

$2 N - t^{2} + t = 0$

Step 4

Solve the equation for $N$ .

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Step 4.1

Move all terms not containing $N$ to the right side of the equation.

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Step 4.1.1

Add $t^{2}$ to both sides of the equation.

$2 N + t = t^{2}$

Step 4.1.2

Subtract $t$ from both sides of the equation.

$2 N = t^{2} - t$

Step 4.2

Divide each term in $2 N = t^{2} - t$ by $2$ and simplify.

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Step 4.2.1

Divide each term in $2 N = t^{2} - t$ by $2$ .

$\frac{2 N}{2} = \frac{t^{2}}{2} + \frac{- t}{2}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $2$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{2 N}{2} = \frac{t^{2}}{2} + \frac{- t}{2}$

Step 4.2.2.1.2

Divide $N$ by $1$ .

$N = \frac{t^{2}}{2} + \frac{- t}{2}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Move the negative in front of the fraction.

$N = \frac{t^{2}}{2} - \frac{t}{2}$