Basic Math Examples

$(\frac{37 \cdot 36}{2}) + (\frac{h \cdot (h - 1)}{2}) - \frac{(37 - h) \cdot (36 - h)}{2} = 720$

Step 1

Simplify $\frac{37 \cdot 36}{2} + \frac{h \cdot (h - 1)}{2} - \frac{(37 - h) \cdot (36 - h)}{2}$ .

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Step 1.1

Combine the numerators over the common denominator.

$\frac{37 \cdot 36 + h \cdot (h - 1) - (37 - h) \cdot (36 - h)}{2} = 720$

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply $37$ by $36$ .

$\frac{1332 + h \cdot (h - 1) - (37 - h) \cdot (36 - h)}{2} = 720$

Step 1.2.2

Apply the distributive property.

$\frac{1332 + h \cdot h + h \cdot - 1 - (37 - h) \cdot (36 - h)}{2} = 720$

Step 1.2.3

Multiply $h$ by $h$ .

$\frac{1332 + h^{2} + h \cdot - 1 - (37 - h) \cdot (36 - h)}{2} = 720$

Step 1.2.4

Move $- 1$ to the left of $h$ .

$\frac{1332 + h^{2} - 1 \cdot h - (37 - h) \cdot (36 - h)}{2} = 720$

Step 1.2.5

Rewrite $- 1 h$ as $- h$ .

$\frac{1332 + h^{2} - h - (37 - h) \cdot (36 - h)}{2} = 720$

Step 1.2.6

Apply the distributive property.

$\frac{1332 + h^{2} - h + (- 1 \cdot 37 - - h) \cdot (36 - h)}{2} = 720$

Step 1.2.7

Multiply $- 1$ by $37$ .

$\frac{1332 + h^{2} - h + (- 37 - - h) \cdot (36 - h)}{2} = 720$

Step 1.2.8

Multiply $- - h$ .

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Step 1.2.8.1

Multiply $- 1$ by $- 1$ .

$\frac{1332 + h^{2} - h + (- 37 + 1 h) \cdot (36 - h)}{2} = 720$

Step 1.2.8.2

Multiply $h$ by $1$ .

$\frac{1332 + h^{2} - h + (- 37 + h) \cdot (36 - h)}{2} = 720$

Step 1.2.9

Expand $(- 37 + h) (36 - h)$ using the FOIL Method.

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Step 1.2.9.1

Apply the distributive property.

$\frac{1332 + h^{2} - h - 37 (36 - h) + h (36 - h)}{2} = 720$

Step 1.2.9.2

Apply the distributive property.

$\frac{1332 + h^{2} - h - 37 \cdot 36 - 37 (- h) + h (36 - h)}{2} = 720$

Step 1.2.9.3

Apply the distributive property.

$\frac{1332 + h^{2} - h - 37 \cdot 36 - 37 (- h) + h \cdot 36 + h (- h)}{2} = 720$

Step 1.2.10

Simplify and combine like terms.

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Step 1.2.10.1

Simplify each term.

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Step 1.2.10.1.1

Multiply $- 37$ by $36$ .

$\frac{1332 + h^{2} - h - 1332 - 37 (- h) + h \cdot 36 + h (- h)}{2} = 720$

Step 1.2.10.1.2

Multiply $- 1$ by $- 37$ .

$\frac{1332 + h^{2} - h - 1332 + 37 h + h \cdot 36 + h (- h)}{2} = 720$

Step 1.2.10.1.3

Move $36$ to the left of $h$ .

$\frac{1332 + h^{2} - h - 1332 + 37 h + 36 \cdot h + h (- h)}{2} = 720$

Step 1.2.10.1.4

Rewrite using the commutative property of multiplication.

$\frac{1332 + h^{2} - h - 1332 + 37 h + 36 h - h \cdot h}{2} = 720$

Step 1.2.10.1.5

Multiply $h$ by $h$ by adding the exponents.

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Step 1.2.10.1.5.1

Move $h$ .

$\frac{1332 + h^{2} - h - 1332 + 37 h + 36 h - (h \cdot h)}{2} = 720$

Step 1.2.10.1.5.2

Multiply $h$ by $h$ .

$\frac{1332 + h^{2} - h - 1332 + 37 h + 36 h - h^{2}}{2} = 720$

Step 1.2.10.2

Add $37 h$ and $36 h$ .

$\frac{1332 + h^{2} - h - 1332 + 73 h - h^{2}}{2} = 720$

Step 1.3

Simplify terms.

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Step 1.3.1

Combine the opposite terms in $1332 + h^{2} - h - 1332 + 73 h - h^{2}$ .

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Step 1.3.1.1

Subtract $1332$ from $1332$ .

$\frac{h^{2} - h + 0 + 73 h - h^{2}}{2} = 720$

Step 1.3.1.2

Add $h^{2} - h$ and $0$ .

$\frac{h^{2} - h + 73 h - h^{2}}{2} = 720$

Step 1.3.1.3

Subtract $h^{2}$ from $h^{2}$ .

$\frac{- h + 73 h + 0}{2} = 720$

Step 1.3.1.4

Add $- h + 73 h$ and $0$ .

$\frac{- h + 73 h}{2} = 720$

Step 1.3.2

Add $- h$ and $73 h$ .

$\frac{72 h}{2} = 720$

Step 1.3.3

Cancel the common factor of $72$ and $2$ .

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Step 1.3.3.1

Factor $2$ out of $72 h$ .

$\frac{2 (36 h)}{2} = 720$

Step 1.3.3.2

Cancel the common factors.

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Step 1.3.3.2.1

Factor $2$ out of $2$ .

$\frac{2 (36 h)}{2 (1)} = 720$

Step 1.3.3.2.2

Cancel the common factor.

$\frac{2 (36 h)}{2 \cdot 1} = 720$

Step 1.3.3.2.3

Rewrite the expression.

$\frac{36 h}{1} = 720$

Step 1.3.3.2.4

Divide $36 h$ by $1$ .

$36 h = 720$

Step 2

Divide each term in $36 h = 720$ by $36$ and simplify.

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Step 2.1

Divide each term in $36 h = 720$ by $36$ .

$\frac{36 h}{36} = \frac{720}{36}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $36$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{36 h}{36} = \frac{720}{36}$

Step 2.2.1.2

Divide $h$ by $1$ .

$h = \frac{720}{36}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $720$ by $36$ .

$h = 20$