Solve 5x-(x-2)^2-3(2x+5)=+4(-1)-(x-1)(x+1)+5

$$5 x - ( x - 2 ) ^ { 2 } - 3 ( 2 x + 5 ) = + 4 ( - 1 ) - ( x - 1 ) ( x + 1 ) + 5$$

Solve for x

$$x=7$$

Steps for Solving Linear Equation

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

$$5x-\left(x^{2}-4x+4\right)-3\left(2x+5\right)=4\left(-1\right)-\left(x-1\right)\left(x+1\right)+5$$

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

$$5x-x^{2}+4x-4-3\left(2x+5\right)=4\left(-1\right)-\left(x-1\right)\left(x+1\right)+5$$

Combine 5x and 4x to get 9x.

$$9x-x^{2}-4-3\left(2x+5\right)=4\left(-1\right)-\left(x-1\right)\left(x+1\right)+5$$

Use the distributive property to multiply -3 by 2x+5.

$$9x-x^{2}-4-6x-15=4\left(-1\right)-\left(x-1\right)\left(x+1\right)+5$$

Combine 9x and -6x to get 3x.

$$3x-x^{2}-4-15=4\left(-1\right)-\left(x-1\right)\left(x+1\right)+5$$

Subtract 15 from -4 to get -19.

$$3x-x^{2}-19=4\left(-1\right)-\left(x-1\right)\left(x+1\right)+5$$

Multiply 4 and -1 to get -4.

$$3x-x^{2}-19=-4-\left(x-1\right)\left(x+1\right)+5$$

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$3x-x^{2}-19=-4-\left(x^{2}-1\right)+5$$

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

$$3x-x^{2}-19=-4-x^{2}+1+5$$

Add -4 and 1 to get -3.

$$3x-x^{2}-19=-3-x^{2}+5$$

Add -3 and 5 to get 2.

$$3x-x^{2}-19=2-x^{2}$$

Add x^{2} to both sides.

$$3x-x^{2}-19+x^{2}=2$$

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

$$3x-19=2$$

Add 19 to both sides.

$$3x=2+19$$

Add 2 and 19 to get 21.

$$3x=21$$

Divide both sides by 3.

$$x=\frac{21}{3}$$

Divide 21 by 3 to get 7.

$$x=7$$