Solve (x+1)^2-(x+2)(x-3)+5x/4-9x/2=25/4

$$( x + 1 ) ^ { 2 } - ( x + 2 ) ( x - 3 ) + \frac { 5 x } { 4 } - \frac { 9 x } { 2 } = \frac { 25 } { 4 }$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 4,2.

$$4\left(\left(x+1\right)^{2}-\left(x+2\right)\left(x-3\right)\right)+5x-2\times 9x=25$$

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

$$4\left(x^{2}+2x+1-\left(x+2\right)\left(x-3\right)\right)+5x-2\times 9x=25$$

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

$$4\left(x^{2}+2x+1-\left(x^{2}-x-6\right)\right)+5x-2\times 9x=25$$

To find the opposite of x^{2}-x-6, find the opposite of each term.

$$4\left(x^{2}+2x+1-x^{2}+x+6\right)+5x-2\times 9x=25$$

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

$$4\left(2x+1+x+6\right)+5x-2\times 9x=25$$

Combine 2x and x to get 3x.

$$4\left(3x+1+6\right)+5x-2\times 9x=25$$

Add 1 and 6 to get 7.

$$4\left(3x+7\right)+5x-2\times 9x=25$$

Use the distributive property to multiply 4 by 3x+7.

$$12x+28+5x-2\times 9x=25$$

Combine 12x and 5x to get 17x.

$$17x+28-2\times 9x=25$$

Multiply -2 and 9 to get -18.

$$17x+28-18x=25$$

Combine 17x and -18x to get -x.

$$-x+28=25$$

Subtract 28 from both sides.

$$-x=25-28$$

Subtract 28 from 25 to get -3.

$$-x=-3$$

Multiply both sides by -1.

$$x=3$$