Solve (3x-1)(5-2x)=(x-7)(3-6x)

$$( 3 x - 1 ) ( 5 - 2 x ) = ( x - 7 ) ( 3 - 6 x )$$

Solve for x

$$x=\frac{4}{7}\approx 0.571428571$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3x-1 by 5-2x and combine like terms.

$$17x-6x^{2}-5=\left(x-7\right)\left(3-6x\right)$$

Use the distributive property to multiply x-7 by 3-6x and combine like terms.

$$17x-6x^{2}-5=45x-6x^{2}-21$$

Subtract 45x from both sides.

$$17x-6x^{2}-5-45x=-6x^{2}-21$$

Combine 17x and -45x to get -28x.

$$-28x-6x^{2}-5=-6x^{2}-21$$

Add 6x^{2} to both sides.

$$-28x-6x^{2}-5+6x^{2}=-21$$

Combine -6x^{2} and 6x^{2} to get 0.

$$-28x-5=-21$$

Add 5 to both sides.

$$-28x=-21+5$$

Add -21 and 5 to get -16.

$$-28x=-16$$

Divide both sides by -28.

$$x=\frac{-16}{-28}$$

Reduce the fraction \frac{-16}{-28} to lowest terms by extracting and canceling out -4.

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