Solve (-6z^229z^26)/(z-6)

Question

Simplify the expression

- \frac{1044 z ^{4}}{z - 6}

Evaluate

\frac{- 6 z ^{2} \times 29 z ^{2} \times 6}{z - 6}

Multiply

More Steps

Multiply the terms

- 6 z^{2} \times 29 z^{2} \times 6

Multiply the terms

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Evaluate

6 \times 29 \times 6

Multiply the terms

174 \times 6

Multiply the numbers

1044

- 1044 z^{2} \times z^{2}

Multiply the terms with the same base by adding their exponents

- 1044 z^{2 + 2}

Add the numbers

- 1044 z^{4}

\frac{- 1044 z ^{4}}{z - 6}

Solution

- \frac{1044 z ^{4}}{z - 6}

Show Solution

z = 6

Evaluate

\frac{- 6 z ^{2} \times 29 z ^{2} \times 6}{z - 6}

To find the excluded values,set the denominators equal to 0

z - 6 = 0

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

z = 0 + 6

Solution

z = 6

Show Solution

z = 0

Evaluate

\frac{- 6 z ^{2} \times 29 z ^{2} \times 6}{z - 6}

To find the roots of the expression,set the expression equal to 0

\frac{- 6 z ^{2} \times 29 z ^{2} \times 6}{z - 6} = 0

Find the domain

More Steps

Evaluate

z - 6 \neq = 0

Move the constant to the right side

z \neq = 0 + 6

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

z \neq = 6

\frac{- 6 z ^{2} \times 29 z ^{2} \times 6}{z - 6} = 0, z \neq = 6

Calculate

\frac{- 6 z ^{2} \times 29 z ^{2} \times 6}{z - 6} = 0

Multiply

More Steps

Multiply the terms

- 6 z^{2} \times 29 z^{2} \times 6

Multiply the terms

More Steps

Evaluate

6 \times 29 \times 6

Multiply the terms

174 \times 6

Multiply the numbers

1044

- 1044 z^{2} \times z^{2}

Multiply the terms with the same base by adding their exponents

- 1044 z^{2 + 2}

Add the numbers

- 1044 z^{4}

\frac{- 1044 z ^{4}}{z - 6} = 0

Cross multiply

- 1044 z^{4} = (z - 6) \times 0

Simplify the equation

- 1044 z^{4} = 0

Change the signs on both sides of the equation

1044 z^{4} = 0

Rewrite the expression

z^{4} = 0

The only way a power can be 0 is when the base equals 0

z = 0

Check if the solution is in the defined range

z = 0, z \neq = 6

Solution

z = 0

Show Solution