Solve (3x-1)^2-5(x-2)-(2x+3)^2-(5x+2)(x-1)=0

$$( 3 x - 1 ) ^ { 2 } - 5 ( x - 2 ) - ( 2 x + 3 ) ^ { 2 } - ( 5 x + 2 ) ( x - 1 ) = 0$$

Solve for x

$$x=\frac{1}{5}=0.2$$

Steps for Solving Linear Equation

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

$$9x^{2}-6x+1-5\left(x-2\right)-\left(2x+3\right)^{2}-\left(5x+2\right)\left(x-1\right)=0$$

Use the distributive property to multiply -5 by x-2.

$$9x^{2}-6x+1-5x+10-\left(2x+3\right)^{2}-\left(5x+2\right)\left(x-1\right)=0$$

Combine -6x and -5x to get -11x.

$$9x^{2}-11x+1+10-\left(2x+3\right)^{2}-\left(5x+2\right)\left(x-1\right)=0$$

Add 1 and 10 to get 11.

$$9x^{2}-11x+11-\left(2x+3\right)^{2}-\left(5x+2\right)\left(x-1\right)=0$$

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

$$9x^{2}-11x+11-\left(4x^{2}+12x+9\right)-\left(5x+2\right)\left(x-1\right)=0$$

To find the opposite of 4x^{2}+12x+9, find the opposite of each term.

$$9x^{2}-11x+11-4x^{2}-12x-9-\left(5x+2\right)\left(x-1\right)=0$$

Combine 9x^{2} and -4x^{2} to get 5x^{2}.

$$5x^{2}-11x+11-12x-9-\left(5x+2\right)\left(x-1\right)=0$$

Combine -11x and -12x to get -23x.

$$5x^{2}-23x+11-9-\left(5x+2\right)\left(x-1\right)=0$$

Subtract 9 from 11 to get 2.

$$5x^{2}-23x+2-\left(5x+2\right)\left(x-1\right)=0$$

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

$$5x^{2}-23x+2-\left(5x^{2}-3x-2\right)=0$$

To find the opposite of 5x^{2}-3x-2, find the opposite of each term.

$$5x^{2}-23x+2-5x^{2}+3x+2=0$$

Combine 5x^{2} and -5x^{2} to get 0.

$$-23x+2+3x+2=0$$

Combine -23x and 3x to get -20x.

$$-20x+2+2=0$$

Add 2 and 2 to get 4.

$$-20x+4=0$$

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$-20x=-4$$

Divide both sides by -20.

$$x=\frac{-4}{-20}$$

Reduce the fraction \frac{-4}{-20} to lowest terms by extracting and canceling out -4.

$$x=\frac{1}{5}$$