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

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

Evaluate

$$\frac{3x^{2}}{2}+\frac{2}{3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.

$$\left(\frac{3x}{2}-\frac{2}{2}\right)^{2}\times \frac{2}{3}+2x$$

Since \frac{3x}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{3x-2}{2}\right)^{2}\times \frac{2}{3}+2x$$

To raise \frac{3x-2}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3x-2\right)^{2}}{2^{2}}\times \frac{2}{3}+2x$$

Multiply \frac{\left(3x-2\right)^{2}}{2^{2}} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3x-2\right)^{2}\times 2}{2^{2}\times 3}+2x$$

Cancel out 2 in both numerator and denominator.

$$\frac{\left(3x-2\right)^{2}}{2\times 3}+2x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x times \frac{2\times 3}{2\times 3}.

$$\frac{\left(3x-2\right)^{2}}{2\times 3}+\frac{2x\times 2\times 3}{2\times 3}$$

Since \frac{\left(3x-2\right)^{2}}{2\times 3} and \frac{2x\times 2\times 3}{2\times 3} have the same denominator, add them by adding their numerators.

$$\frac{\left(3x-2\right)^{2}+2x\times 2\times 3}{2\times 3}$$

Do the multiplications in \left(3x-2\right)^{2}+2x\times 2\times 3.

$$\frac{9x^{2}-12x+4+12x}{2\times 3}$$

Combine like terms in 9x^{2}-12x+4+12x.

$$\frac{9x^{2}+4}{2\times 3}$$

Expand 2\times 3.

$$\frac{9x^{2}+4}{6}$$

Expand

$$\frac{3x^{2}}{2}+\frac{2}{3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.

$$\left(\frac{3x}{2}-\frac{2}{2}\right)^{2}\times \frac{2}{3}+2x$$

Since \frac{3x}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{3x-2}{2}\right)^{2}\times \frac{2}{3}+2x$$

To raise \frac{3x-2}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3x-2\right)^{2}}{2^{2}}\times \frac{2}{3}+2x$$

Multiply \frac{\left(3x-2\right)^{2}}{2^{2}} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(3x-2\right)^{2}\times 2}{2^{2}\times 3}+2x$$

Cancel out 2 in both numerator and denominator.

$$\frac{\left(3x-2\right)^{2}}{2\times 3}+2x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x times \frac{2\times 3}{2\times 3}.

$$\frac{\left(3x-2\right)^{2}}{2\times 3}+\frac{2x\times 2\times 3}{2\times 3}$$

Since \frac{\left(3x-2\right)^{2}}{2\times 3} and \frac{2x\times 2\times 3}{2\times 3} have the same denominator, add them by adding their numerators.

$$\frac{\left(3x-2\right)^{2}+2x\times 2\times 3}{2\times 3}$$

Do the multiplications in \left(3x-2\right)^{2}+2x\times 2\times 3.

$$\frac{9x^{2}-12x+4+12x}{2\times 3}$$

Combine like terms in 9x^{2}-12x+4+12x.

$$\frac{9x^{2}+4}{2\times 3}$$

Expand 2\times 3.

$$\frac{9x^{2}+4}{6}$$