Solve (5-2x)(x-3)-6.5x=(1-2x)(x-1)+12.5

$$(5-2x)(x-3)-6.5x=(1-2x)(x-1)+12.5$$

Solve for x

$$x = \frac{53}{3} = 17\frac{2}{3} \approx 17.666666667$$

Steps for Solving Linear Equation

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

$$11x-15-2x^{2}-6.5x=\left(1-2x\right)\left(x-1\right)+12.5$$

Combine 11x and -6.5x to get 4.5x.

$$4.5x-15-2x^{2}=\left(1-2x\right)\left(x-1\right)+12.5$$

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

$$4.5x-15-2x^{2}=3x-1-2x^{2}+12.5$$

Add -1 and 12.5 to get 11.5.

$$4.5x-15-2x^{2}=3x+11.5-2x^{2}$$

Subtract 3x from both sides.

$$4.5x-15-2x^{2}-3x=11.5-2x^{2}$$

Combine 4.5x and -3x to get 1.5x.

$$1.5x-15-2x^{2}=11.5-2x^{2}$$

Add 2x^{2} to both sides.

$$1.5x-15-2x^{2}+2x^{2}=11.5$$

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

$$1.5x-15=11.5$$

Add 15 to both sides.

$$1.5x=11.5+15$$

Add 11.5 and 15 to get 26.5.

$$1.5x=26.5$$

Divide both sides by 1.5.

$$x=\frac{26.5}{1.5}$$

Expand \frac{26.5}{1.5} by multiplying both numerator and the denominator by 10.

$$x=\frac{265}{15}$$

Reduce the fraction \frac{265}{15} to lowest terms by extracting and canceling out 5.

$$x=\frac{53}{3}$$