Solve left(3x-2right)left(2-3xright)-2x+1=9left(2x-x^2right)+4left(x+3right)

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

Solve for x

$$x = -\frac{5}{4} = -1\frac{1}{4} = -1.25$$

Steps for Solving Linear Equation

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

$$12x-9x^{2}-4-2x+1=9\left(2x-x^{2}\right)+4\left(x+3\right)$$

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

$$10x-9x^{2}-4+1=9\left(2x-x^{2}\right)+4\left(x+3\right)$$

Add -4 and 1 to get -3.

$$10x-9x^{2}-3=9\left(2x-x^{2}\right)+4\left(x+3\right)$$

Use the distributive property to multiply 9 by 2x-x^{2}.

$$10x-9x^{2}-3=18x-9x^{2}+4\left(x+3\right)$$

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

$$10x-9x^{2}-3=18x-9x^{2}+4x+12$$

Combine 18x and 4x to get 22x.

$$10x-9x^{2}-3=22x-9x^{2}+12$$

Subtract 22x from both sides.

$$10x-9x^{2}-3-22x=-9x^{2}+12$$

Combine 10x and -22x to get -12x.

$$-12x-9x^{2}-3=-9x^{2}+12$$

Add 9x^{2} to both sides.

$$-12x-9x^{2}-3+9x^{2}=12$$

Combine -9x^{2} and 9x^{2} to get 0.

$$-12x-3=12$$

Add 3 to both sides.

$$-12x=12+3$$

Add 12 and 3 to get 15.

$$-12x=15$$

Divide both sides by -12.

$$x=\frac{15}{-12}$$

Reduce the fraction \frac{15}{-12} to lowest terms by extracting and canceling out 3.

$$x=-\frac{5}{4}$$