Solve (5-2x)(x-3)-65x=(1-2x)(x-1)+125

$$(5-2x)(x-3)-65x=(1-2x)(x-1)+125$$

Solve for x

$$x = -\frac{139}{57} = -2\frac{25}{57} \approx -2.438596491$$

Steps for Solving Linear Equation

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

$$11x-15-2x^{2}-65x=\left(1-2x\right)\left(x-1\right)+125$$

Combine 11x and -65x to get -54x.

$$-54x-15-2x^{2}=\left(1-2x\right)\left(x-1\right)+125$$

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

$$-54x-15-2x^{2}=3x-1-2x^{2}+125$$

Add -1 and 125 to get 124.

$$-54x-15-2x^{2}=3x+124-2x^{2}$$

Subtract 3x from both sides.

$$-54x-15-2x^{2}-3x=124-2x^{2}$$

Combine -54x and -3x to get -57x.

$$-57x-15-2x^{2}=124-2x^{2}$$

Add 2x^{2} to both sides.

$$-57x-15-2x^{2}+2x^{2}=124$$

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

$$-57x-15=124$$

Add 15 to both sides.

$$-57x=124+15$$

Add 124 and 15 to get 139.

$$-57x=139$$

Divide both sides by -57.

$$x=\frac{139}{-57}$$

Fraction \frac{139}{-57} can be rewritten as -\frac{139}{57} by extracting the negative sign.

$$x=-\frac{139}{57}$$