Solve by Factoring 10x^2-25x+15=0

$10 x^{2} - 25 x + 15 = 0$

Step 1

Factor $5$ out of $10 x^{2} - 25 x + 15$ .

Factor $5$ out of $10 x^{2}$ .

$5 (2 x^{2}) - 25 x + 15 = 0$

Factor $5$ out of $- 25 x$ .

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

Factor $5$ out of $15$ .

$5 (2 x^{2}) + 5 (- 5 x) + 5 (3) = 0$

Factor $5$ out of $5 (2 x^{2}) + 5 (- 5 x)$ .

$5 (2 x^{2} - 5 x) + 5 (3) = 0$

Factor $5$ out of $5 (2 x^{2} - 5 x) + 5 (3)$ .

$5 (2 x^{2} - 5 x + 3) = 0$

Step 2

Factor.

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 $a \cdot c = 2 \cdot 3 = 6$ and whose sum is $b = - 5$ .

Factor $- 5$ out of $- 5 x$ .

$5 (2 x^{2} - 5 x + 3) = 0$

Rewrite $- 5$ as $- 2$ plus $- 3$

$5 (2 x^{2} + (- 2 - 3) x + 3) = 0$

Apply the distributive property.

$5 (2 x^{2} - 2 x - 3 x + 3) = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$5 ((2 x^{2} - 2 x) - 3 x + 3) = 0$

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

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

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

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

Remove unnecessary parentheses.

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

Step 3

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

$x - 1 = 0$

$2 x - 3 = 0$

Step 4

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

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

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

Step 5

Set $2 x - 3$ equal to $0$ and solve for $x$ .

Set $2 x - 3$ equal to $0$ .

$2 x - 3 = 0$

Solve $2 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$2 x = 3$

Divide each term in $2 x = 3$ by $2$ and simplify.

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Divide $x$ by $1$ .

$x = \frac{3}{2}$

Step 6

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

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

Solve by Factoring 10x^2-25x+15=0

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