Basic Math Examples

${(z^{2} + 6 z)}^{2} + 14 (z^{2} + 6) + 5 = 0$

Step 1

Simplify ${(z^{2} + 6 z)}^{2} + 14 (z^{2} + 6) + 5$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Rewrite ${(z^{2} + 6 z)}^{2}$ as $(z^{2} + 6 z) (z^{2} + 6 z)$ .

$(z^{2} + 6 z) (z^{2} + 6 z) + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.2

Expand $(z^{2} + 6 z) (z^{2} + 6 z)$ using the FOIL Method.

Tap for more steps...

Step 1.1.2.1

Apply the distributive property.

$z^{2} (z^{2} + 6 z) + 6 z (z^{2} + 6 z) + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.2.2

Apply the distributive property.

$z^{2} z^{2} + z^{2} (6 z) + 6 z (z^{2} + 6 z) + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.2.3

Apply the distributive property.

$z^{2} z^{2} + z^{2} (6 z) + 6 z \cdot z^{2} + 6 z (6 z) + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.3

Simplify and combine like terms.

Tap for more steps...

Step 1.1.3.1

Simplify each term.

Tap for more steps...

Step 1.1.3.1.1

Multiply $z^{2}$ by $z^{2}$ by adding the exponents.

Tap for more steps...

Step 1.1.3.1.1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$z^{2 + 2} + z^{2} (6 z) + 6 z \cdot z^{2} + 6 z (6 z) + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.3.1.1.2

Add $2$ and $2$ .

$z^{4} + z^{2} (6 z) + 6 z \cdot z^{2} + 6 z (6 z) + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.3.1.2

Rewrite using the commutative property of multiplication.

$z^{4} + 6 z^{2} z + 6 z \cdot z^{2} + 6 z (6 z) + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.3.1.3

Multiply $z^{2}$ by $z$ by adding the exponents.

Tap for more steps...

Step 1.1.3.1.3.1

Move $z$ .

$z^{4} + 6 (z \cdot z^{2}) + 6 z \cdot z^{2} + 6 z (6 z) + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.3.1.3.2

Multiply $z$ by $z^{2}$ .

Tap for more steps...

Step 1.1.3.1.3.2.1

Raise $z$ to the power of $1$ .

$z^{4} + 6 (z^{1} z^{2}) + 6 z \cdot z^{2} + 6 z (6 z) + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.3.1.3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$z^{4} + 6 z^{1 + 2} + 6 z \cdot z^{2} + 6 z (6 z) + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.3.1.3.3

Add $1$ and $2$ .

$z^{4} + 6 z^{3} + 6 z \cdot z^{2} + 6 z (6 z) + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.3.1.4

Multiply $z$ by $z^{2}$ by adding the exponents.

Tap for more steps...

Step 1.1.3.1.4.1

Move $z^{2}$ .

$z^{4} + 6 z^{3} + 6 (z^{2} z) + 6 z (6 z) + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.3.1.4.2

Multiply $z^{2}$ by $z$ .

Tap for more steps...

Step 1.1.3.1.4.2.1

Raise $z$ to the power of $1$ .

$z^{4} + 6 z^{3} + 6 (z^{2} z^{1}) + 6 z (6 z) + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.3.1.4.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$z^{4} + 6 z^{3} + 6 z^{2 + 1} + 6 z (6 z) + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.3.1.4.3

Add $2$ and $1$ .

$z^{4} + 6 z^{3} + 6 z^{3} + 6 z (6 z) + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.3.1.5

Rewrite using the commutative property of multiplication.

$z^{4} + 6 z^{3} + 6 z^{3} + 6 \cdot 6 z \cdot z + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.3.1.6

Multiply $z$ by $z$ by adding the exponents.

Tap for more steps...

Step 1.1.3.1.6.1

Move $z$ .

$z^{4} + 6 z^{3} + 6 z^{3} + 6 \cdot 6 (z \cdot z) + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.3.1.6.2

Multiply $z$ by $z$ .

$z^{4} + 6 z^{3} + 6 z^{3} + 6 \cdot 6 z^{2} + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.3.1.7

Multiply $6$ by $6$ .

$z^{4} + 6 z^{3} + 6 z^{3} + 36 z^{2} + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.3.2

Add $6 z^{3}$ and $6 z^{3}$ .

$z^{4} + 12 z^{3} + 36 z^{2} + 14 (z^{2} + 6) + 5 = 0$

Step 1.1.4

Apply the distributive property.

$z^{4} + 12 z^{3} + 36 z^{2} + 14 z^{2} + 14 \cdot 6 + 5 = 0$

Step 1.1.5

Multiply $14$ by $6$ .

$z^{4} + 12 z^{3} + 36 z^{2} + 14 z^{2} + 84 + 5 = 0$

Step 1.2

Simplify by adding terms.

Tap for more steps...

Step 1.2.1

Add $36 z^{2}$ and $14 z^{2}$ .

$z^{4} + 12 z^{3} + 50 z^{2} + 84 + 5 = 0$

Step 1.2.2

Add $84$ and $5$ .

$z^{4} + 12 z^{3} + 50 z^{2} + 89 = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

No solution