Solve by Factoring 5x^2-3x+8=3x^2+8x-1

$5 x^{2} - 3 x + 8 = 3 x^{2} + 8 x - 1$

Step 1

Move all the expressions to the left side of the equation.

Subtract $3 x^{2}$ from both sides of the equation.

$5 x^{2} - 3 x + 8 - 3 x^{2} = 8 x - 1$

Subtract $8 x$ from both sides of the equation.

$5 x^{2} - 3 x + 8 - 3 x^{2} - 8 x = - 1$

Add $1$ to both sides of the equation.

$5 x^{2} - 3 x + 8 - 3 x^{2} - 8 x + 1 = 0$

Step 2

Simplify $5 x^{2} - 3 x + 8 - 3 x^{2} - 8 x + 1$ .

Subtract $3 x^{2}$ from $5 x^{2}$ .

$2 x^{2} - 3 x + 8 - 8 x + 1 = 0$

Subtract $8 x$ from $- 3 x$ .

$2 x^{2} - 11 x + 8 + 1 = 0$

Add $8$ and $1$ .

$2 x^{2} - 11 x + 9 = 0$

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 $a \cdot c = 2 \cdot 9 = 18$ and whose sum is $b = - 11$ .

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

$2 x^{2} - 11 x + 9 = 0$

Rewrite $- 11$ as $- 2$ plus $- 9$

$2 x^{2} + (- 2 - 9) x + 9 = 0$

Apply the distributive property.

$2 x^{2} - 2 x - 9 x + 9 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 2 x) - 9 x + 9 = 0$

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

$2 x (x - 1) - 9 (x - 1) = 0$

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

$(x - 1) (2 x - 9) = 0$

Step 4

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

$x - 1 = 0$

$2 x - 9 = 0$

Step 5

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 6

Set $2 x - 9$ equal to $0$ and solve for $x$ .

Set $2 x - 9$ equal to $0$ .

$2 x - 9 = 0$

Solve $2 x - 9 = 0$ for $x$ .

Add $9$ to both sides of the equation.

$2 x = 9$

Divide each term in $2 x = 9$ by $2$ and simplify.

Divide each term in $2 x = 9$ by $2$ .

$\frac{2 x}{2} = \frac{9}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{9}{2}$

Divide $x$ by $1$ .

$x = \frac{9}{2}$

Step 7

The final solution is all the values that make $(x - 1) (2 x - 9) = 0$ true.

$x = 1, \frac{9}{2}$

Solve by Factoring 5x^2-3x+8=3x^2+8x-1

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