Algebra Examples

$- 4 k^{2} - 8 k - 3 = - 3 - 5 k^{2}$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Add $3$ to both sides of the equation.

$- 4 k^{2} - 8 k - 3 + 3 = - 5 k^{2}$

Step 1.2

Add $5 k^{2}$ to both sides of the equation.

$- 4 k^{2} - 8 k - 3 + 3 + 5 k^{2} = 0$

Step 2

Simplify $- 4 k^{2} - 8 k - 3 + 3 + 5 k^{2}$ .

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Step 2.1

Combine the opposite terms in $- 4 k^{2} - 8 k - 3 + 3 + 5 k^{2}$ .

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Step 2.1.1

Add $- 3$ and $3$ .

$- 4 k^{2} - 8 k + 0 + 5 k^{2} = 0$

Step 2.1.2

Add $- 4 k^{2} - 8 k$ and $0$ .

$- 4 k^{2} - 8 k + 5 k^{2} = 0$

Step 2.2

Add $- 4 k^{2}$ and $5 k^{2}$ .

$k^{2} - 8 k = 0$

Step 3

Factor $k$ out of $k^{2} - 8 k$ .

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Step 3.1

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

$k \cdot k - 8 k = 0$

Step 3.2

Factor $k$ out of $- 8 k$ .

$k \cdot k + k \cdot - 8 = 0$

Step 3.3

Factor $k$ out of $k \cdot k + k \cdot - 8$ .

$k (k - 8) = 0$

Step 4

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

$k = 0$

$k - 8 = 0$

Step 5

Set $k$ equal to $0$ .

$k = 0$

Step 6

Set $k - 8$ equal to $0$ and solve for $k$ .

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Step 6.1

Set $k - 8$ equal to $0$ .

$k - 8 = 0$

Step 6.2

Add $8$ to both sides of the equation.

$k = 8$

Step 7

The final solution is all the values that make $k (k - 8) = 0$ true.

$k = 0, 8$