Find the Roots (Zeros) -6x^2+x-6=-8x^2

$- 6 x^{2} + x - 6 = - 8 x^{2}$

Step 1

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

Add $8 x^{2}$ to both sides of the equation.

$- 6 x^{2} + x - 6 + 8 x^{2} = 0$

Add $- 6 x^{2}$ and $8 x^{2}$ .

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

Step 2

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 $a \cdot c = 2 \cdot - 6 = - 12$ and whose sum is $b = 1$ .

Multiply by $1$ .

$2 x^{2} + 1 x - 6 = 0$

Rewrite $1$ as $- 3$ plus $4$

$2 x^{2} + (- 3 + 4) x - 6 = 0$

Apply the distributive property.

$2 x^{2} - 3 x + 4 x - 6 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 3 x) + 4 x - 6 = 0$

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

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

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

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

Step 3

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

$2 x - 3 = 0$

$x + 2 = 0$

Step 4

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 5

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 6

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

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

Step 7

Find the Roots (Zeros) -6x^2+x-6=-8x^2

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