Basic Math Examples

$7 k^{2} - 6 k + 3 = 3$

Step 1

Subtract $3$ from both sides of the equation.

$7 k^{2} - 6 k + 3 - 3 = 0$

Step 2

Combine the opposite terms in $7 k^{2} - 6 k + 3 - 3$ .

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Step 2.1

Subtract $3$ from $3$ .

$7 k^{2} - 6 k + 0 = 0$

Step 2.2

Add $7 k^{2} - 6 k$ and $0$ .

$7 k^{2} - 6 k = 0$

Step 3

Factor $k$ out of $7 k^{2} - 6 k$ .

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Step 3.1

Factor $k$ out of $7 k^{2}$ .

$k (7 k) - 6 k = 0$

Step 3.2

Factor $k$ out of $- 6 k$ .

$k (7 k) + k \cdot - 6 = 0$

Step 3.3

Factor $k$ out of $k (7 k) + k \cdot - 6$ .

$k (7 k - 6) = 0$

Step 4

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

$k = 0$

$7 k - 6 = 0$

Step 5

Set $k$ equal to $0$ .

$k = 0$

Step 6

Set $7 k - 6$ equal to $0$ and solve for $k$ .

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Step 6.1

Set $7 k - 6$ equal to $0$ .

$7 k - 6 = 0$

Step 6.2

Solve $7 k - 6 = 0$ for $k$ .

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Step 6.2.1

Add $6$ to both sides of the equation.

$7 k = 6$

Step 6.2.2

Divide each term in $7 k = 6$ by $7$ and simplify.

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Step 6.2.2.1

Divide each term in $7 k = 6$ by $7$ .

$\frac{7 k}{7} = \frac{6}{7}$

Step 6.2.2.2

Simplify the left side.

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Step 6.2.2.2.1

Cancel the common factor of $7$ .

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Step 6.2.2.2.1.1

Cancel the common factor.

$\frac{7 k}{7} = \frac{6}{7}$

Step 6.2.2.2.1.2

Divide $k$ by $1$ .

$k = \frac{6}{7}$

Step 7

The final solution is all the values that make $k (7 k - 6) = 0$ true.

$k = 0, \frac{6}{7}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$k = 0, \frac{6}{7}$

Decimal Form:

$k = 0, 0.\overline{857142}$