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

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

Solve for x

$$x = -\frac{11}{10} = -1\frac{1}{10} = -1.1$$

Steps for Solving Linear Equation

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

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

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

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

To find the opposite of -1+4x^{2}, find the opposite of each term.

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

Add 9 and 1 to get 10.

$$4x^{2}+12x+10-4x^{2}=x^{2}-\left(x-1\right)^{2}$$

Combine 4x^{2} and -4x^{2} to get 0.

$$12x+10=x^{2}-\left(x-1\right)^{2}$$

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

$$12x+10=x^{2}-\left(x^{2}-2x+1\right)$$

To find the opposite of x^{2}-2x+1, find the opposite of each term.

$$12x+10=x^{2}-x^{2}+2x-1$$

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

$$12x+10=2x-1$$

Subtract 2x from both sides.

$$12x+10-2x=-1$$

Combine 12x and -2x to get 10x.

$$10x+10=-1$$

Subtract 10 from both sides.

$$10x=-1-10$$

Subtract 10 from -1 to get -11.

$$10x=-11$$

Divide both sides by 10.

$$x=\frac{-11}{10}$$

Fraction \frac{-11}{10} can be rewritten as -\frac{11}{10} by extracting the negative sign.

$$x=-\frac{11}{10}$$