Basic Math Examples

$(7 y + 13) (3 t + 20) = 180$

Step 1

Divide each term in $(7 y + 13) (3 t + 20) = 180$ by $7 y + 13$ and simplify.

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Step 1.1

Divide each term in $(7 y + 13) (3 t + 20) = 180$ by $7 y + 13$ .

$\frac{(7 y + 13) (3 t + 20)}{7 y + 13} = \frac{180}{7 y + 13}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $7 y + 13$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{(7 y + 13) (3 t + 20)}{7 y + 13} = \frac{180}{7 y + 13}$

Step 1.2.1.2

Divide $3 t + 20$ by $1$ .

$3 t + 20 = \frac{180}{7 y + 13}$

Step 2

Subtract $20$ from both sides of the equation.

$3 t = \frac{180}{7 y + 13} - 20$

Step 3

Divide each term in $3 t = \frac{180}{7 y + 13} - 20$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 t = \frac{180}{7 y + 13} - 20$ by $3$ .

$\frac{3 t}{3} = \frac{\frac{180}{7 y + 13}}{3} + \frac{- 20}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 t}{3} = \frac{\frac{180}{7 y + 13}}{3} + \frac{- 20}{3}$

Step 3.2.1.2

Divide $t$ by $1$ .

$t = \frac{\frac{180}{7 y + 13}}{3} + \frac{- 20}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Combine the numerators over the common denominator.

$t = \frac{\frac{180}{7 y + 13} - 20}{3}$

Step 3.3.2

To write $- 20$ as a fraction with a common denominator, multiply by $\frac{7 y + 13}{7 y + 13}$ .

$t = \frac{\frac{180}{7 y + 13} - 20 \cdot \frac{7 y + 13}{7 y + 13}}{3}$

Step 3.3.3

Simplify terms.

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Step 3.3.3.1

Combine $- 20$ and $\frac{7 y + 13}{7 y + 13}$ .

$t = \frac{\frac{180}{7 y + 13} + \frac{- 20 (7 y + 13)}{7 y + 13}}{3}$

Step 3.3.3.2

Combine the numerators over the common denominator.

$t = \frac{\frac{180 - 20 (7 y + 13)}{7 y + 13}}{3}$

Step 3.3.4

Simplify the numerator.

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Step 3.3.4.1

Factor $20$ out of $180 - 20 (7 y + 13)$ .

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Step 3.3.4.1.1

Factor $20$ out of $180$ .

$t = \frac{\frac{20 (9) - 20 (7 y + 13)}{7 y + 13}}{3}$

Step 3.3.4.1.2

Factor $20$ out of $- 20 (7 y + 13)$ .

$t = \frac{\frac{20 (9) + 20 (- (7 y + 13))}{7 y + 13}}{3}$

Step 3.3.4.1.3

Factor $20$ out of $20 (9) + 20 (- (7 y + 13))$ .

$t = \frac{\frac{20 (9 - (7 y + 13))}{7 y + 13}}{3}$

Step 3.3.4.2

Apply the distributive property.

$t = \frac{\frac{20 (9 - (7 y) - 1 \cdot 13)}{7 y + 13}}{3}$

Step 3.3.4.3

Multiply $7$ by $- 1$ .

$t = \frac{\frac{20 (9 - 7 y - 1 \cdot 13)}{7 y + 13}}{3}$

Step 3.3.4.4

Multiply $- 1$ by $13$ .

$t = \frac{\frac{20 (9 - 7 y - 13)}{7 y + 13}}{3}$

Step 3.3.4.5

Subtract $13$ from $9$ .

$t = \frac{\frac{20 (- 7 y - 4)}{7 y + 13}}{3}$

Step 3.3.5

Simplify with factoring out.

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Step 3.3.5.1

Factor $- 1$ out of $- 7 y$ .

$t = \frac{\frac{20 (- (7 y) - 4)}{7 y + 13}}{3}$

Step 3.3.5.2

Rewrite $- 4$ as $- 1 (4)$ .

$t = \frac{\frac{20 (- (7 y) - 1 (4))}{7 y + 13}}{3}$

Step 3.3.5.3

Factor $- 1$ out of $- (7 y) - 1 (4)$ .

$t = \frac{\frac{20 (- (7 y + 4))}{7 y + 13}}{3}$

Step 3.3.5.4

Simplify the expression.

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Step 3.3.5.4.1

Rewrite $- (7 y + 4)$ as $- 1 (7 y + 4)$ .

$t = \frac{\frac{20 (- 1 (7 y + 4))}{7 y + 13}}{3}$

Step 3.3.5.4.2

Move the negative in front of the fraction.

$t = \frac{- \frac{20 (7 y + 4)}{7 y + 13}}{3}$

Step 3.3.6

Multiply the numerator by the reciprocal of the denominator.

$t = - \frac{20 (7 y + 4)}{7 y + 13} \cdot \frac{1}{3}$

Step 3.3.7

Multiply $\frac{1}{3}$ by $\frac{20 (7 y + 4)}{7 y + 13}$ .

$t = - \frac{20 (7 y + 4)}{3 (7 y + 13)}$