Solve 3x(2-5x)+3/4(2+2/3x)=

$$3 x ( 2 - 5 x ) + \frac { 3 } { 4 } ( 2 + \frac { 2 } { 3 } x ) =$$

Evaluate

$$-15x^{2}+\frac{13x}{2}+\frac{3}{2}$$

Solution Steps

Use the distributive property to multiply 3x by 2-5x.

$$6x-15x^{2}+\frac{3}{4}\left(2+\frac{2}{3}x\right)$$

Use the distributive property to multiply \frac{3}{4} by 2+\frac{2}{3}x.

$$6x-15x^{2}+\frac{3}{4}\times 2+\frac{3}{4}\times \frac{2}{3}x$$

Express \frac{3}{4}\times 2 as a single fraction.

$$6x-15x^{2}+\frac{3\times 2}{4}+\frac{3}{4}\times \frac{2}{3}x$$

Multiply 3 and 2 to get 6.

$$6x-15x^{2}+\frac{6}{4}+\frac{3}{4}\times \frac{2}{3}x$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$6x-15x^{2}+\frac{3}{2}+\frac{3}{4}\times \frac{2}{3}x$$

Multiply \frac{3}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$6x-15x^{2}+\frac{3}{2}+\frac{3\times 2}{4\times 3}x$$

Cancel out 3 in both numerator and denominator.

$$6x-15x^{2}+\frac{3}{2}+\frac{2}{4}x$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$6x-15x^{2}+\frac{3}{2}+\frac{1}{2}x$$

Combine 6x and \frac{1}{2}x to get \frac{13}{2}x.

$$\frac{13}{2}x-15x^{2}+\frac{3}{2}$$

Expand

$$-15x^{2}+\frac{13x}{2}+\frac{3}{2}$$

Solution Steps

Use the distributive property to multiply 3x by 2-5x.

$$6x-15x^{2}+\frac{3}{4}\left(2+\frac{2}{3}x\right)$$

Use the distributive property to multiply \frac{3}{4} by 2+\frac{2}{3}x.

$$6x-15x^{2}+\frac{3}{4}\times 2+\frac{3}{4}\times \frac{2}{3}x$$

Express \frac{3}{4}\times 2 as a single fraction.

$$6x-15x^{2}+\frac{3\times 2}{4}+\frac{3}{4}\times \frac{2}{3}x$$

Multiply 3 and 2 to get 6.

$$6x-15x^{2}+\frac{6}{4}+\frac{3}{4}\times \frac{2}{3}x$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$6x-15x^{2}+\frac{3}{2}+\frac{3}{4}\times \frac{2}{3}x$$

Multiply \frac{3}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$6x-15x^{2}+\frac{3}{2}+\frac{3\times 2}{4\times 3}x$$

Cancel out 3 in both numerator and denominator.

$$6x-15x^{2}+\frac{3}{2}+\frac{2}{4}x$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$6x-15x^{2}+\frac{3}{2}+\frac{1}{2}x$$

Combine 6x and \frac{1}{2}x to get \frac{13}{2}x.

$$\frac{13}{2}x-15x^{2}+\frac{3}{2}$$