Pre-Algebra Examples

${(t + 4)}^{2} (- 13 t - 64) + 32 = 0$

Step 1

Simplify ${(t + 4)}^{2} (- 13 t - 64) + 32$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Rewrite ${(t + 4)}^{2}$ as $(t + 4) (t + 4)$ .

$(t + 4) (t + 4) (- 13 t - 64) + 32 = 0$

Step 1.1.2

Expand $(t + 4) (t + 4)$ using the FOIL Method.

Tap for more steps...

Step 1.1.2.1

Apply the distributive property.

$(t (t + 4) + 4 (t + 4)) (- 13 t - 64) + 32 = 0$

Step 1.1.2.2

Apply the distributive property.

$(t \cdot t + t \cdot 4 + 4 (t + 4)) (- 13 t - 64) + 32 = 0$

Step 1.1.2.3

Apply the distributive property.

$(t \cdot t + t \cdot 4 + 4 t + 4 \cdot 4) (- 13 t - 64) + 32 = 0$

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 $t$ by $t$ .

$(t^{2} + t \cdot 4 + 4 t + 4 \cdot 4) (- 13 t - 64) + 32 = 0$

Step 1.1.3.1.2

Move $4$ to the left of $t$ .

$(t^{2} + 4 \cdot t + 4 t + 4 \cdot 4) (- 13 t - 64) + 32 = 0$

Step 1.1.3.1.3

Multiply $4$ by $4$ .

$(t^{2} + 4 t + 4 t + 16) (- 13 t - 64) + 32 = 0$

Step 1.1.3.2

Add $4 t$ and $4 t$ .

$(t^{2} + 8 t + 16) (- 13 t - 64) + 32 = 0$

Step 1.1.4

Expand $(t^{2} + 8 t + 16) (- 13 t - 64)$ by multiplying each term in the first expression by each term in the second expression.

$t^{2} (- 13 t) + t^{2} \cdot - 64 + 8 t (- 13 t) + 8 t \cdot - 64 + 16 (- 13 t) + 16 \cdot - 64 + 32 = 0$

Step 1.1.5

Simplify each term.

Tap for more steps...

Step 1.1.5.1

Rewrite using the commutative property of multiplication.

$- 13 t^{2} t + t^{2} \cdot - 64 + 8 t (- 13 t) + 8 t \cdot - 64 + 16 (- 13 t) + 16 \cdot - 64 + 32 = 0$

Step 1.1.5.2

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

Tap for more steps...

Step 1.1.5.2.1

Move $t$ .

$- 13 (t \cdot t^{2}) + t^{2} \cdot - 64 + 8 t (- 13 t) + 8 t \cdot - 64 + 16 (- 13 t) + 16 \cdot - 64 + 32 = 0$

Step 1.1.5.2.2

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

Tap for more steps...

Step 1.1.5.2.2.1

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

$- 13 (t^{1} t^{2}) + t^{2} \cdot - 64 + 8 t (- 13 t) + 8 t \cdot - 64 + 16 (- 13 t) + 16 \cdot - 64 + 32 = 0$

Step 1.1.5.2.2.2

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

$- 13 t^{1 + 2} + t^{2} \cdot - 64 + 8 t (- 13 t) + 8 t \cdot - 64 + 16 (- 13 t) + 16 \cdot - 64 + 32 = 0$

Step 1.1.5.2.3

Add $1$ and $2$ .

$- 13 t^{3} + t^{2} \cdot - 64 + 8 t (- 13 t) + 8 t \cdot - 64 + 16 (- 13 t) + 16 \cdot - 64 + 32 = 0$

Step 1.1.5.3

Move $- 64$ to the left of $t^{2}$ .

$- 13 t^{3} - 64 \cdot t^{2} + 8 t (- 13 t) + 8 t \cdot - 64 + 16 (- 13 t) + 16 \cdot - 64 + 32 = 0$

Step 1.1.5.4

Rewrite using the commutative property of multiplication.

$- 13 t^{3} - 64 t^{2} + 8 \cdot - 13 t \cdot t + 8 t \cdot - 64 + 16 (- 13 t) + 16 \cdot - 64 + 32 = 0$

Step 1.1.5.5

Multiply $t$ by $t$ by adding the exponents.

Tap for more steps...

Step 1.1.5.5.1

Move $t$ .

$- 13 t^{3} - 64 t^{2} + 8 \cdot - 13 (t \cdot t) + 8 t \cdot - 64 + 16 (- 13 t) + 16 \cdot - 64 + 32 = 0$

Step 1.1.5.5.2

Multiply $t$ by $t$ .

$- 13 t^{3} - 64 t^{2} + 8 \cdot - 13 t^{2} + 8 t \cdot - 64 + 16 (- 13 t) + 16 \cdot - 64 + 32 = 0$

Step 1.1.5.6

Multiply $8$ by $- 13$ .

$- 13 t^{3} - 64 t^{2} - 104 t^{2} + 8 t \cdot - 64 + 16 (- 13 t) + 16 \cdot - 64 + 32 = 0$

Step 1.1.5.7

Multiply $- 64$ by $8$ .

$- 13 t^{3} - 64 t^{2} - 104 t^{2} - 512 t + 16 (- 13 t) + 16 \cdot - 64 + 32 = 0$

Step 1.1.5.8

Multiply $- 13$ by $16$ .

$- 13 t^{3} - 64 t^{2} - 104 t^{2} - 512 t - 208 t + 16 \cdot - 64 + 32 = 0$

Step 1.1.5.9

Multiply $16$ by $- 64$ .

$- 13 t^{3} - 64 t^{2} - 104 t^{2} - 512 t - 208 t - 1024 + 32 = 0$

Step 1.1.6

Subtract $104 t^{2}$ from $- 64 t^{2}$ .

$- 13 t^{3} - 168 t^{2} - 512 t - 208 t - 1024 + 32 = 0$

Step 1.1.7

Subtract $208 t$ from $- 512 t$ .

$- 13 t^{3} - 168 t^{2} - 720 t - 1024 + 32 = 0$

Step 1.2

Add $- 1024$ and $32$ .

$- 13 t^{3} - 168 t^{2} - 720 t - 992 = 0$

Step 2

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

$t \approx - 2.89759908$

Step 3