Solve by Factoring 2x^2+8x=5x+20

$2 x^{2} + 8 x = 5 x + 20$

Step 1

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

Subtract $5 x$ from both sides of the equation.

$2 x^{2} + 8 x - 5 x = 20$

Subtract $20$ from both sides of the equation.

$2 x^{2} + 8 x - 5 x - 20 = 0$

Step 2

Subtract $5 x$ from $8 x$ .

$2 x^{2} + 3 x - 20 = 0$

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 $a \cdot c = 2 \cdot - 20 = - 40$ and whose sum is $b = 3$ .

Factor $3$ out of $3 x$ .

$2 x^{2} + 3 (x) - 20 = 0$

Rewrite $3$ as $- 5$ plus $8$

$2 x^{2} + (- 5 + 8) x - 20 = 0$

Apply the distributive property.

$2 x^{2} - 5 x + 8 x - 20 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 5 x) + 8 x - 20 = 0$

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

$x (2 x - 5) + 4 (2 x - 5) = 0$

Factor the polynomial by factoring out the greatest common factor, $2 x - 5$ .

$(2 x - 5) (x + 4) = 0$

Step 4

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

$2 x - 5 = 0$

$x + 4 = 0$

Step 5

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

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

$2 x - 5 = 0$

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

Add $5$ to both sides of the equation.

$2 x = 5$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 6

Set $x + 4$ equal to $0$ and solve for $x$ .

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 7

The final solution is all the values that make $(2 x - 5) (x + 4) = 0$ true.

$x = \frac{5}{2}, - 4$

Solve by Factoring 2x^2+8x=5x+20

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