Solve 2*(x-1)*(2+x)-3/2-(x+2)^2=x*(3-sqrt[5]{-1})-3-x/3

$$\frac { 2 \cdot ( x - 1 ) \cdot ( 2 + x ) - 3 } { 2 } - ( x + 2 ) ^ { 2 } = x \cdot ( 3 - \sqrt[ 5 ] { - 1 } ) - \frac { 3 - x } { 3 }$$

Solve for x

$$x=-\frac{39}{44}\approx -0.886363636$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$3\left(2\left(x-1\right)\left(2+x\right)-3\right)-6\left(x+2\right)^{2}=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

Use the distributive property to multiply 2 by x-1.

$$3\left(\left(2x-2\right)\left(2+x\right)-3\right)-6\left(x+2\right)^{2}=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

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

$$3\left(2x+2x^{2}-4-3\right)-6\left(x+2\right)^{2}=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

Subtract 3 from -4 to get -7.

$$3\left(2x+2x^{2}-7\right)-6\left(x+2\right)^{2}=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

Use the distributive property to multiply 3 by 2x+2x^{2}-7.

$$6x+6x^{2}-21-6\left(x+2\right)^{2}=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

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

$$6x+6x^{2}-21-6\left(x^{2}+4x+4\right)=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

Use the distributive property to multiply -6 by x^{2}+4x+4.

$$6x+6x^{2}-21-6x^{2}-24x-24=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

Combine 6x^{2} and -6x^{2} to get 0.

$$6x-21-24x-24=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

Combine 6x and -24x to get -18x.

$$-18x-21-24=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

Subtract 24 from -21 to get -45.

$$-18x-45=6x\left(3-\sqrt[5]{-1}\right)-2\left(3-x\right)$$

Calculate \sqrt[5]{-1} and get -1.

$$-18x-45=6x\left(3-\left(-1\right)\right)-2\left(3-x\right)$$

The opposite of -1 is 1.

$$-18x-45=6x\left(3+1\right)-2\left(3-x\right)$$

Add 3 and 1 to get 4.

$$-18x-45=6x\times 4-2\left(3-x\right)$$

Multiply 6 and 4 to get 24.

$$-18x-45=24x-2\left(3-x\right)$$

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

$$-18x-45=24x-6+2x$$

Combine 24x and 2x to get 26x.

$$-18x-45=26x-6$$

Subtract 26x from both sides.

$$-18x-45-26x=-6$$

Combine -18x and -26x to get -44x.

$$-44x-45=-6$$

Add 45 to both sides.

$$-44x=-6+45$$

Add -6 and 45 to get 39.

$$-44x=39$$

Divide both sides by -44.

$$x=\frac{39}{-44}$$

Fraction \frac{39}{-44} can be rewritten as -\frac{39}{44} by extracting the negative sign.

$$x=-\frac{39}{44}$$