Find the Roots (Zeros) 2x^2+10x=3x+15

$2 x^{2} + 10 x = 3 x + 15$

Move all terms containing $x$ to the left side of the equation.

Subtract $3 x$ from both sides of the equation.

$2 x^{2} + 10 x - 3 x = 15$

Subtract $3 x$ from $10 x$ .

$2 x^{2} + 7 x = 15$

Subtract $15$ from both sides of the equation.

$2 x^{2} + 7 x - 15 = 0$

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 $a \cdot c = 2 \cdot - 15 = - 30$ and whose sum is $b = 7$ .

Factor $7$ out of $7 x$ .

$2 x^{2} + 7 (x) - 15 = 0$

Rewrite $7$ as $- 3$ plus $10$

$2 x^{2} + (- 3 + 10) x - 15 = 0$

Apply the distributive property.

$2 x^{2} - 3 x + 10 x - 15 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 3 x) + 10 x - 15 = 0$

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

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

Factor the polynomial by factoring out the greatest common factor, $2 x - 3$ .

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

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

$2 x - 3 = 0$

$x + 5 = 0$

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 $1$ .

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

Set $x + 5$ equal to $0$ and solve for $x$ .

Set $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

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

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

Find the Roots (Zeros) 2x^2+10x=3x+15

Related Questions

Support LCMGCF.com by disabling your adblocker.