Basic Math Examples

$3 t = d (5 - t)$

Step 1

Simplify $d (5 - t)$ .

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Step 1.1

Apply the distributive property.

$3 t = d \cdot 5 + d (- t)$

Step 1.2

Reorder.

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Step 1.2.1

Move $5$ to the left of $d$ .

$3 t = 5 \cdot d + d (- t)$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$3 t = 5 d - d t$

Step 2

Add $d t$ to both sides of the equation.

$3 t + d t = 5 d$

Step 3

Factor $t$ out of $3 t + d t$ .

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Step 3.1

Factor $t$ out of $3 t$ .

$t \cdot 3 + d t = 5 d$

Step 3.2

Factor $t$ out of $d t$ .

$t \cdot 3 + t d = 5 d$

Step 3.3

Factor $t$ out of $t \cdot 3 + t d$ .

$t (3 + d) = 5 d$

Step 4

Divide each term in $t (3 + d) = 5 d$ by $3 + d$ and simplify.

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Step 4.1

Divide each term in $t (3 + d) = 5 d$ by $3 + d$ .

$\frac{t (3 + d)}{3 + d} = \frac{5 d}{3 + d}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3 + d$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{t (3 + d)}{3 + d} = \frac{5 d}{3 + d}$

Step 4.2.1.2

Divide $t$ by $1$ .

$t = \frac{5 d}{3 + d}$