Solve left(2x-4right)left(3-6xright)=left(3x-5right)left(10-4xright)

$$\left( 2x-4 \right) \left( 3-6x \right) = \left( 3x-5 \right) \left( 10-4x \right)$$

Solve for x

$$x = \frac{19}{10} = 1\frac{9}{10} = 1.9$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-4 by 3-6x and combine like terms.

$$30x-12x^{2}-12=\left(3x-5\right)\left(10-4x\right)$$

Use the distributive property to multiply 3x-5 by 10-4x and combine like terms.

$$30x-12x^{2}-12=50x-12x^{2}-50$$

Subtract 50x from both sides.

$$30x-12x^{2}-12-50x=-12x^{2}-50$$

Combine 30x and -50x to get -20x.

$$-20x-12x^{2}-12=-12x^{2}-50$$

Add 12x^{2} to both sides.

$$-20x-12x^{2}-12+12x^{2}=-50$$

Combine -12x^{2} and 12x^{2} to get 0.

$$-20x-12=-50$$

Add 12 to both sides.

$$-20x=-50+12$$

Add -50 and 12 to get -38.

$$-20x=-38$$

Divide both sides by -20.

$$x=\frac{-38}{-20}$$

Reduce the fraction \frac{-38}{-20} to lowest terms by extracting and canceling out -2.

$$x=\frac{19}{10}$$