Algebra Examples

$2 k (- 3 k + 4) + 6 (k^{2} + 10) = k (4 k + 8) - 2 k (2 k + 5)$

Step 1

Since $k$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$k (4 k + 8) - 2 k (2 k + 5) = 2 k (- 3 k + 4) + 6 (k^{2} + 10)$

Step 2

Simplify $k (4 k + 8) - 2 k (2 k + 5)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$k (4 k) + k \cdot 8 - 2 k (2 k + 5) = 2 k (- 3 k + 4) + 6 (k^{2} + 10)$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$4 k \cdot k + k \cdot 8 - 2 k (2 k + 5) = 2 k (- 3 k + 4) + 6 (k^{2} + 10)$

Step 2.1.3

Move $8$ to the left of $k$ .

$4 k \cdot k + 8 \cdot k - 2 k (2 k + 5) = 2 k (- 3 k + 4) + 6 (k^{2} + 10)$

Step 2.1.4

Multiply $k$ by $k$ by adding the exponents.

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Step 2.1.4.1

Move $k$ .

$4 (k \cdot k) + 8 \cdot k - 2 k (2 k + 5) = 2 k (- 3 k + 4) + 6 (k^{2} + 10)$

Step 2.1.4.2

Multiply $k$ by $k$ .

$4 k^{2} + 8 \cdot k - 2 k (2 k + 5) = 2 k (- 3 k + 4) + 6 (k^{2} + 10)$

$4 k^{2} + 8 k - 2 k (2 k + 5) = 2 k (- 3 k + 4) + 6 (k^{2} + 10)$

Step 2.1.5

Apply the distributive property.

$4 k^{2} + 8 k - 2 k (2 k) - 2 k \cdot 5 = 2 k (- 3 k + 4) + 6 (k^{2} + 10)$

Step 2.1.6

Rewrite using the commutative property of multiplication.

$4 k^{2} + 8 k - 2 \cdot 2 k \cdot k - 2 k \cdot 5 = 2 k (- 3 k + 4) + 6 (k^{2} + 10)$

Step 2.1.7

Multiply $5$ by $- 2$ .

$4 k^{2} + 8 k - 2 \cdot 2 k \cdot k - 10 k = 2 k (- 3 k + 4) + 6 (k^{2} + 10)$

Step 2.1.8

Simplify each term.

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Step 2.1.8.1

Multiply $k$ by $k$ by adding the exponents.

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Step 2.1.8.1.1

Move $k$ .

$4 k^{2} + 8 k - 2 \cdot 2 (k \cdot k) - 10 k = 2 k (- 3 k + 4) + 6 (k^{2} + 10)$

Step 2.1.8.1.2

Multiply $k$ by $k$ .

$4 k^{2} + 8 k - 2 \cdot 2 k^{2} - 10 k = 2 k (- 3 k + 4) + 6 (k^{2} + 10)$

Step 2.1.8.2

Multiply $- 2$ by $2$ .

$4 k^{2} + 8 k - 4 k^{2} - 10 k = 2 k (- 3 k + 4) + 6 (k^{2} + 10)$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Combine the opposite terms in $4 k^{2} + 8 k - 4 k^{2} - 10 k$ .

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Step 2.2.1.1

Subtract $4 k^{2}$ from $4 k^{2}$ .

$8 k + 0 - 10 k = 2 k (- 3 k + 4) + 6 (k^{2} + 10)$

Step 2.2.1.2

Add $8 k$ and $0$ .

$8 k - 10 k = 2 k (- 3 k + 4) + 6 (k^{2} + 10)$

Step 2.2.2

Subtract $10 k$ from $8 k$ .

$- 2 k = 2 k (- 3 k + 4) + 6 (k^{2} + 10)$

Step 3

Simplify $2 k (- 3 k + 4) + 6 (k^{2} + 10)$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$- 2 k = 2 k (- 3 k) + 2 k \cdot 4 + 6 (k^{2} + 10)$

Step 3.1.2

Rewrite using the commutative property of multiplication.

$- 2 k = 2 \cdot - 3 k \cdot k + 2 k \cdot 4 + 6 (k^{2} + 10)$

Step 3.1.3

Multiply $4$ by $2$ .

$- 2 k = 2 \cdot - 3 k \cdot k + 8 k + 6 (k^{2} + 10)$

Step 3.1.4

Simplify each term.

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Step 3.1.4.1

Multiply $k$ by $k$ by adding the exponents.

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Step 3.1.4.1.1

Move $k$ .

$- 2 k = 2 \cdot - 3 (k \cdot k) + 8 k + 6 (k^{2} + 10)$

Step 3.1.4.1.2

Multiply $k$ by $k$ .

$- 2 k = 2 \cdot - 3 k^{2} + 8 k + 6 (k^{2} + 10)$

Step 3.1.4.2

Multiply $2$ by $- 3$ .

$- 2 k = - 6 k^{2} + 8 k + 6 (k^{2} + 10)$

Step 3.1.5

Apply the distributive property.

$- 2 k = - 6 k^{2} + 8 k + 6 k^{2} + 6 \cdot 10$

Step 3.1.6

Multiply $6$ by $10$ .

$- 2 k = - 6 k^{2} + 8 k + 6 k^{2} + 60$

Step 3.2

Combine the opposite terms in $- 6 k^{2} + 8 k + 6 k^{2} + 60$ .

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Step 3.2.1

Add $- 6 k^{2}$ and $6 k^{2}$ .

$- 2 k = 8 k + 0 + 60$

Step 3.2.2

Add $8 k$ and $0$ .

$- 2 k = 8 k + 60$

Step 4

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

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Step 4.1

Subtract $8 k$ from both sides of the equation.

$- 2 k - 8 k = 60$

Step 4.2

Subtract $8 k$ from $- 2 k$ .

$- 10 k = 60$

Step 5

Divide each term in $- 10 k = 60$ by $- 10$ and simplify.

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Step 5.1

Divide each term in $- 10 k = 60$ by $- 10$ .

$\frac{- 10 k}{- 10} = \frac{60}{- 10}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 10$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 10 k}{- 10} = \frac{60}{- 10}$

Step 5.2.1.2

Divide $k$ by $1$ .

$k = \frac{60}{- 10}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $60$ by $- 10$ .

$k = - 6$