Solve (3x-2)*(2-3x)-2x+1=9*(2x-x^2)+4-(x+3)

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

Solve for x

$$x=-\frac{4}{7}\approx -0.571428571$$

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}.

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

To find the opposite of x+3, find the opposite of each term.

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

Combine 18x and -x to get 17x.

$$10x-9x^{2}-3=17x-9x^{2}+4-3$$

Subtract 3 from 4 to get 1.

$$10x-9x^{2}-3=17x-9x^{2}+1$$

Subtract 17x from both sides.

$$10x-9x^{2}-3-17x=-9x^{2}+1$$

Combine 10x and -17x to get -7x.

$$-7x-9x^{2}-3=-9x^{2}+1$$

Add 9x^{2} to both sides.

$$-7x-9x^{2}-3+9x^{2}=1$$

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

$$-7x-3=1$$

Add 3 to both sides.

$$-7x=1+3$$

Add 1 and 3 to get 4.

$$-7x=4$$

Divide both sides by -7.

$$x=\frac{4}{-7}$$

Fraction \frac{4}{-7} can be rewritten as -\frac{4}{7} by extracting the negative sign.

$$x=-\frac{4}{7}$$