Solve (n-3)(n-4)(n-5)=720

Question

Solve the equation

n = 13

Evaluate

(n - 3) (n - 4) (n - 5) = 720

Expand the expression

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Evaluate

(n - 3) (n - 4) (n - 5)

Multiply the terms

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Evaluate

(n - 3) (n - 4)

Apply the distributive property

n \times n - n \times 4 - 3 n - (- 3 \times 4)

Multiply the terms

n^{2} - n \times 4 - 3 n - (- 3 \times 4)

Use the commutative property to reorder the terms

n^{2} - 4 n - 3 n - (- 3 \times 4)

Multiply the numbers

n^{2} - 4 n - 3 n - (- 12)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

n^{2} - 4 n - 3 n + 12

Subtract the terms

n^{2} - 7 n + 12

(n^{2} - 7 n + 12) (n - 5)

Apply the distributive property

n^{2} \times n - n^{2} \times 5 - 7 n \times n - (- 7 n \times 5) + 12 n - 12 \times 5

Multiply the terms

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Evaluate

n^{2} \times n

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

n^{2 + 1}

Add the numbers

n^{3}

n^{3} - n^{2} \times 5 - 7 n \times n - (- 7 n \times 5) + 12 n - 12 \times 5

Use the commutative property to reorder the terms

n^{3} - 5 n^{2} - 7 n \times n - (- 7 n \times 5) + 12 n - 12 \times 5

Multiply the terms

n^{3} - 5 n^{2} - 7 n^{2} - (- 7 n \times 5) + 12 n - 12 \times 5

Multiply the numbers

n^{3} - 5 n^{2} - 7 n^{2} - (- 35 n) + 12 n - 12 \times 5

Multiply the numbers

n^{3} - 5 n^{2} - 7 n^{2} - (- 35 n) + 12 n - 60

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

n^{3} - 5 n^{2} - 7 n^{2} + 35 n + 12 n - 60

Subtract the terms

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Evaluate

- 5 n^{2} - 7 n^{2}

Collect like terms by calculating the sum or difference of their coefficients

(- 5 - 7) n^{2}

Subtract the numbers

- 12 n^{2}

n^{3} - 12 n^{2} + 35 n + 12 n - 60

Add the terms

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Evaluate

35 n + 12 n

Collect like terms by calculating the sum or difference of their coefficients

(35 + 12) n

Add the numbers

47 n

n^{3} - 12 n^{2} + 47 n - 60

n^{3} - 12 n^{2} + 47 n - 60 = 720

Move the expression to the left side

n^{3} - 12 n^{2} + 47 n - 60 - 720 = 0

Subtract the numbers

n^{3} - 12 n^{2} + 47 n - 780 = 0

Factor the expression

(n - 13) (n^{2} + n + 60) = 0

Separate the equation into 2 possible cases

n - 13 = 0 n^{2} + n + 60 = 0

Solve the equation

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Evaluate

n - 13 = 0

Move the constant to the right-hand side and change its sign

n = 0 + 13

Removing 0 doesn't change the value,so remove it from the expression

n = 13

n = 13 n^{2} + n + 60 = 0

Solve the equation

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Evaluate

n^{2} + n + 60 = 0

Substitute a= 1,b= 1 and c= 60 into the quadratic formula n = \frac{- b \pm b ^{2} - 4 a c}{2 a}

n = \frac{- 1 \pm 1 ^{2} - 4 \times 60}{2}

Simplify the expression

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Evaluate

1^{2} - 4 \times 60

1 raised to any power equals to 1

1 - 4 \times 60

Multiply the numbers

1 - 240

Subtract the numbers

- 239

n = \frac{- 1 \pm - 239}{2}

The expression is undefined in the set of real numbers

n \in / R

n = 13 n \in / R

Solution

n = 13

Show Solution

Solve the equation

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