Solve by Factoring 7x^2-6x+3=3

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

Step 1

Subtract $3$ from both sides of the equation.

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

Step 2

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

Subtract $3$ from $3$ .

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

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

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

Step 3

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

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

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

Factor $x$ out of $- 6 x$ .

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

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

$x (7 x - 6) = 0$

Step 4

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

$x = 0$

$7 x - 6 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

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

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

$7 x - 6 = 0$

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

Add $6$ to both sides of the equation.

$7 x = 6$

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

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

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

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 7

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

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