Solve by Factoring 17x^2-11x+2=2x^2

$17 x^{2} - 11 x + 2 = 2 x^{2}$

Step 1

Subtract $2 x^{2}$ from both sides of the equation.

$17 x^{2} - 11 x + 2 - 2 x^{2} = 0$

Step 2

Subtract $2 x^{2}$ from $17 x^{2}$ .

$15 x^{2} - 11 x + 2 = 0$

Step 3

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 15 \cdot 2 = 30$ and whose sum is $b = - 11$ .

Factor $- 11$ out of $- 11 x$ .

$15 x^{2} - 11 x + 2 = 0$

Rewrite $- 11$ as $- 5$ plus $- 6$

$15 x^{2} + (- 5 - 6) x + 2 = 0$

Apply the distributive property.

$15 x^{2} - 5 x - 6 x + 2 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(15 x^{2} - 5 x) - 6 x + 2 = 0$

Factor out the greatest common factor (GCF) from each group.

$5 x (3 x - 1) - 2 (3 x - 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $3 x - 1$ .

$(3 x - 1) (5 x - 2) = 0$

Step 4

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

$3 x - 1 = 0$

$5 x - 2 = 0$

Step 5

Set $3 x - 1$ equal to $0$ and solve for $x$ .

Set $3 x - 1$ equal to $0$ .

$3 x - 1 = 0$

Solve $3 x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$3 x = 1$

Divide each term in $3 x = 1$ by $3$ and simplify.

Divide each term in $3 x = 1$ by $3$ .

$\frac{3 x}{3} = \frac{1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{1}{3}$

Divide $x$ by $1$ .

$x = \frac{1}{3}$

Step 6

Set $5 x - 2$ equal to $0$ and solve for $x$ .

Set $5 x - 2$ equal to $0$ .

$5 x - 2 = 0$

Solve $5 x - 2 = 0$ for $x$ .

Add $2$ to both sides of the equation.

$5 x = 2$

Divide each term in $5 x = 2$ by $5$ and simplify.

Divide each term in $5 x = 2$ by $5$ .

$\frac{5 x}{5} = \frac{2}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{2}{5}$

Divide $x$ by $1$ .

$x = \frac{2}{5}$

Step 7

The final solution is all the values that make $(3 x - 1) (5 x - 2) = 0$ true.

$x = \frac{1}{3}, \frac{2}{5}$

Solve by Factoring 17x^2-11x+2=2x^2

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