Solve by Factoring 2x(x-3)=4x^2-7x

$2 x (x - 3) = 4 x^{2} - 7 x$

Step 1

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

Subtract $4 x^{2}$ from both sides of the equation.

$2 x (x - 3) - 4 x^{2} = - 7 x$

Add $7 x$ to both sides of the equation.

$2 x (x - 3) - 4 x^{2} + 7 x = 0$

Step 2

Simplify $2 x (x - 3) - 4 x^{2} + 7 x$ .

Simplify each term.

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 3 - 4 x^{2} + 7 x = 0$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 (x \cdot x) + 2 x \cdot - 3 - 4 x^{2} + 7 x = 0$

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot - 3 - 4 x^{2} + 7 x = 0$

Multiply $- 3$ by $2$ .

$2 x^{2} - 6 x - 4 x^{2} + 7 x = 0$

Subtract $4 x^{2}$ from $2 x^{2}$ .

$- 2 x^{2} - 6 x + 7 x = 0$

Add $- 6 x$ and $7 x$ .

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

Step 3

Factor $x$ out of $- 2 x^{2} + x$ .

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

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

Raise $x$ to the power of $1$ .

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

Factor $x$ out of $x^{1}$ .

$x (- 2 x) + x \cdot 1 = 0$

Factor $x$ out of $x (- 2 x) + x \cdot 1$ .

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

Step 4

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

$x = 0$

$- 2 x + 1 = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $- 2 x + 1$ equal to $0$ and solve for $x$ .

Set $- 2 x + 1$ equal to $0$ .

$- 2 x + 1 = 0$

Solve $- 2 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$- 2 x = - 1$

Divide each term in $- 2 x = - 1$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 1$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 1}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 1}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 1}{- 2}$

Simplify the right side.

Dividing two negative values results in a positive value.

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

Step 7

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

$x = 0, \frac{1}{2}$

Solve by Factoring 2x(x-3)=4x^2-7x

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