Algebra Examples

$(t - 2) (t + 5) = t - 2 (t + 5)$

Step 1

Simplify $(t - 2) (t + 5)$ .

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Step 1.1

Rewrite.

$0 + 0 + (t - 2) (t + 5) = t - 2 (t + 5)$

Step 1.2

Simplify by adding zeros.

$(t - 2) (t + 5) = t - 2 (t + 5)$

Step 1.3

Expand $(t - 2) (t + 5)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$t (t + 5) - 2 (t + 5) = t - 2 (t + 5)$

Step 1.3.2

Apply the distributive property.

$t \cdot t + t \cdot 5 - 2 (t + 5) = t - 2 (t + 5)$

Step 1.3.3

Apply the distributive property.

$t \cdot t + t \cdot 5 - 2 t - 2 \cdot 5 = t - 2 (t + 5)$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $t$ by $t$ .

$t^{2} + t \cdot 5 - 2 t - 2 \cdot 5 = t - 2 (t + 5)$

Step 1.4.1.2

Move $5$ to the left of $t$ .

$t^{2} + 5 \cdot t - 2 t - 2 \cdot 5 = t - 2 (t + 5)$

Step 1.4.1.3

Multiply $- 2$ by $5$ .

$t^{2} + 5 t - 2 t - 10 = t - 2 (t + 5)$

Step 1.4.2

Subtract $2 t$ from $5 t$ .

$t^{2} + 3 t - 10 = t - 2 (t + 5)$

Step 2

Simplify $t - 2 (t + 5)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$t^{2} + 3 t - 10 = t - 2 t - 2 \cdot 5$

Step 2.1.2

Multiply $- 2$ by $5$ .

$t^{2} + 3 t - 10 = t - 2 t - 10$

Step 2.2

Subtract $2 t$ from $t$ .

$t^{2} + 3 t - 10 = - t - 10$

Step 3

Move all terms containing $t$ to the left side of the equation.

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Step 3.1

Add $t$ to both sides of the equation.

$t^{2} + 3 t - 10 + t = - 10$

Step 3.2

Add $3 t$ and $t$ .

$t^{2} + 4 t - 10 = - 10$

Step 4

Add $10$ to both sides of the equation.

$t^{2} + 4 t - 10 + 10 = 0$

Step 5

Combine the opposite terms in $t^{2} + 4 t - 10 + 10$ .

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Step 5.1

Add $- 10$ and $10$ .

$t^{2} + 4 t + 0 = 0$

Step 5.2

Add $t^{2} + 4 t$ and $0$ .

$t^{2} + 4 t = 0$

Step 6

Factor $t$ out of $t^{2} + 4 t$ .

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Step 6.1

Factor $t$ out of $t^{2}$ .

$t \cdot t + 4 t = 0$

Step 6.2

Factor $t$ out of $4 t$ .

$t \cdot t + t \cdot 4 = 0$

Step 6.3

Factor $t$ out of $t \cdot t + t \cdot 4$ .

$t (t + 4) = 0$

Step 7

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$t = 0$

$t + 4 = 0$

Step 8

Set $t$ equal to $0$ .

$t = 0$

Step 9

Set $t + 4$ equal to $0$ and solve for $t$ .

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Step 9.1

Set $t + 4$ equal to $0$ .

$t + 4 = 0$

Step 9.2

Subtract $4$ from both sides of the equation.

$t = - 4$

Step 10

The final solution is all the values that make $t (t + 4) = 0$ true.

$t = 0, - 4$