Solve (1-3x)^2+(2x-1)^2=13(x-1)(x+1)

$$( 1 - 3 x ) ^ { 2 } + ( 2 x - 1 ) ^ { 2 } = 13 ( x - 1 ) ( x + 1 )$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-3x\right)^{2}.

$$1-6x+9x^{2}+\left(2x-1\right)^{2}=13\left(x-1\right)\left(x+1\right)$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-1\right)^{2}.

$$1-6x+9x^{2}+4x^{2}-4x+1=13\left(x-1\right)\left(x+1\right)$$

Combine 9x^{2} and 4x^{2} to get 13x^{2}.

$$1-6x+13x^{2}-4x+1=13\left(x-1\right)\left(x+1\right)$$

Combine -6x and -4x to get -10x.

$$1-10x+13x^{2}+1=13\left(x-1\right)\left(x+1\right)$$

Add 1 and 1 to get 2.

$$2-10x+13x^{2}=13\left(x-1\right)\left(x+1\right)$$

Use the distributive property to multiply 13 by x-1.

$$2-10x+13x^{2}=\left(13x-13\right)\left(x+1\right)$$

Use the distributive property to multiply 13x-13 by x+1 and combine like terms.

$$2-10x+13x^{2}=13x^{2}-13$$

Subtract 13x^{2} from both sides.

$$2-10x+13x^{2}-13x^{2}=-13$$

Combine 13x^{2} and -13x^{2} to get 0.

$$2-10x=-13$$

Subtract 2 from both sides.

$$-10x=-13-2$$

Subtract 2 from -13 to get -15.

$$-10x=-15$$

Divide both sides by -10.

$$x=\frac{-15}{-10}$$

Reduce the fraction \frac{-15}{-10} to lowest terms by extracting and canceling out -5.

$$x=\frac{3}{2}$$