Solve A=2x(3-5x/2)+3x(2x^2/3+x)

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

Solve for A

$$A=2x\left(x^{2}-x+3\right)$$

Solution Steps

Use the distributive property to multiply 2x by 3-\frac{5x}{2}.

$$A=6x+2x\left(-\frac{5x}{2}\right)+3x\left(\frac{2x^{2}}{3}+x\right)$$

Express 2\left(-\frac{5x}{2}\right) as a single fraction.

$$A=6x+\frac{-2\times 5x}{2}x+3x\left(\frac{2x^{2}}{3}+x\right)$$

Cancel out 2 and 2.

$$A=6x-5xx+3x\left(\frac{2x^{2}}{3}+x\right)$$

Multiply x and x to get x^{2}.

$$A=6x-5x^{2}+3x\left(\frac{2x^{2}}{3}+x\right)$$

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

$$A=6x-5x^{2}+3x\times \frac{2x^{2}}{3}+3x^{2}$$

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

$$A=6x-5x^{2}+\frac{3\times 2x^{2}}{3}x+3x^{2}$$

Cancel out 3 and 3.

$$A=6x-5x^{2}+2x^{2}x+3x^{2}$$

Combine -5x^{2} and 3x^{2} to get -2x^{2}.

$$A=6x-2x^{2}+2x^{2}x$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$A=6x-2x^{2}+2x^{3}$$

Solve for x

$$x=\frac{4^{\frac{2}{3}}\left(\sqrt[3]{3\sqrt{3\left(27A^{2}-100A+396\right)}+27A-50}+\sqrt[3]{-3\sqrt{3\left(27A^{2}-100A+396\right)}+27A-50}+\sqrt[3]{4}\right)}{12}$$