Solve by Factoring 3x(x-2)=5x^2-7x

$3 x (x - 2) = 5 x^{2} - 7 x$

Step 1

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

Subtract $5 x^{2}$ from both sides of the equation.

$3 x (x - 2) - 5 x^{2} = - 7 x$

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

$3 x (x - 2) - 5 x^{2} + 7 x = 0$

Step 2

Simplify $3 x (x - 2) - 5 x^{2} + 7 x$ .

Simplify each term.

Apply the distributive property.

$3 x \cdot x + 3 x \cdot - 2 - 5 x^{2} + 7 x = 0$

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

Move $x$ .

$3 (x \cdot x) + 3 x \cdot - 2 - 5 x^{2} + 7 x = 0$

Multiply $x$ by $x$ .

$3 x^{2} + 3 x \cdot - 2 - 5 x^{2} + 7 x = 0$

Multiply $- 2$ by $3$ .

$3 x^{2} - 6 x - 5 x^{2} + 7 x = 0$

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

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

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 3x(x-2)=5x^2-7x

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