Solve 9z^3-27z^2-100z^300

Question

Simplify the expression

9 z^{3} - 27 z^{2}

Evaluate

9 z^{3} - 27 z^{2} - 100 z^{3} \times 0

Any expression multiplied by 0 equals 0

9 z^{3} - 27 z^{2} - 0

Solution

9 z^{3} - 27 z^{2}

Show Solution

9 z^{2} (z - 3)

Evaluate

9 z^{3} - 27 z^{2} - 100 z^{3} \times 0

Multiply

More Steps

Multiply the terms

100 z^{3} \times 0

Any expression multiplied by 0 equals 0

0 \times z^{3}

Any expression multiplied by 0 equals 0

0

9 z^{3} - 27 z^{2} - 0

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

9 z^{3} - 27 z^{2}

Rewrite the expression

9 z^{2} \times z - 9 z^{2} \times 3

Solution

9 z^{2} (z - 3)

Show Solution

z_{1} = 0, z_{2} = 3

Evaluate

9 z^{3} - 27 z^{2} - 100 z^{3} \times 0

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

9 z^{3} - 27 z^{2} - 100 z^{3} \times 0 = 0

Multiply

More Steps

Multiply the terms

100 z^{3} \times 0

Any expression multiplied by 0 equals 0

0 \times z^{3}

Any expression multiplied by 0 equals 0

0

9 z^{3} - 27 z^{2} - 0 = 0

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

9 z^{3} - 27 z^{2} = 0

Factor the expression

9 z^{2} (z - 3) = 0

Divide both sides

z^{2} (z - 3) = 0

Separate the equation into 2 possible cases

z^{2} = 0 z - 3 = 0

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

z = 0 z - 3 = 0

Solve the equation

More Steps

Evaluate

z - 3 = 0

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

z = 0 + 3

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

z = 3

z = 0 z = 3

Solution

z_{1} = 0, z_{2} = 3

Show Solution