Solve by Factoring 9x^2-10x=x^2+4x

$9 x^{2} - 10 x = x^{2} + 4 x$

Step 1

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

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

$9 x^{2} - 10 x - x^{2} = 4 x$

Subtract $4 x$ from both sides of the equation.

$9 x^{2} - 10 x - x^{2} - 4 x = 0$

Step 2

Simplify $9 x^{2} - 10 x - x^{2} - 4 x$ .

Subtract $x^{2}$ from $9 x^{2}$ .

$8 x^{2} - 10 x - 4 x = 0$

Subtract $4 x$ from $- 10 x$ .

$8 x^{2} - 14 x = 0$

Step 3

Factor $2 x$ out of $8 x^{2} - 14 x$ .

Factor $2 x$ out of $8 x^{2}$ .

$2 x (4 x) - 14 x = 0$

Factor $2 x$ out of $- 14 x$ .

$2 x (4 x) + 2 x (- 7) = 0$

Factor $2 x$ out of $2 x (4 x) + 2 x (- 7)$ .

$2 x (4 x - 7) = 0$

Step 4

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

$x = 0$

$4 x - 7 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $4 x - 7$ equal to $0$ and solve for $x$ .

Set $4 x - 7$ equal to $0$ .

$4 x - 7 = 0$

Solve $4 x - 7 = 0$ for $x$ .

Add $7$ to both sides of the equation.

$4 x = 7$

Divide each term in $4 x = 7$ by $4$ and simplify.

Divide each term in $4 x = 7$ by $4$ .

$\frac{4 x}{4} = \frac{7}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{7}{4}$

Divide $x$ by $1$ .

$x = \frac{7}{4}$

Step 7

The final solution is all the values that make $2 x (4 x - 7) = 0$ true.

$x = 0, \frac{7}{4}$

Solve by Factoring 9x^2-10x=x^2+4x

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