Solve g:x-2(x-3)^2+8x-12

$$g : x - 2 ( x - 3 ) ^ { 2 } + 8 x - 12$$

Evaluate

$$-2x^{2}+20x+\frac{g}{x}-30$$

Short Solution Steps

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

$$\frac{g}{x}-\frac{2\left(x-3\right)^{2}x}{x}+8x-12$$

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

$$\frac{g-2\left(x-3\right)^{2}x}{x}+8x-12$$

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

$$\frac{g-2x^{3}+12x^{2}-18x}{x}+8x-12$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 8x-12 times \frac{x}{x}.

$$\frac{g-2x^{3}+12x^{2}-18x}{x}+\frac{\left(8x-12\right)x}{x}$$

Since \frac{g-2x^{3}+12x^{2}-18x}{x} and \frac{\left(8x-12\right)x}{x} have the same denominator, add them by adding their numerators.

$$\frac{g-2x^{3}+12x^{2}-18x+\left(8x-12\right)x}{x}$$

Do the multiplications in g-2x^{3}+12x^{2}-18x+\left(8x-12\right)x.

$$\frac{g-2x^{3}+12x^{2}-18x+8x^{2}-12x}{x}$$

Combine like terms in g-2x^{3}+12x^{2}-18x+8x^{2}-12x.

$$\frac{-2x^{3}+g+20x^{2}-30x}{x}$$

Expand

$$-2x^{2}+20x+\frac{g}{x}-30$$

Short Solution Steps

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

$$\frac{g}{x}-\frac{2\left(x-3\right)^{2}x}{x}+8x-12$$

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

$$\frac{g-2\left(x-3\right)^{2}x}{x}+8x-12$$

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

$$\frac{g-2x^{3}+12x^{2}-18x}{x}+8x-12$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 8x-12 times \frac{x}{x}.

$$\frac{g-2x^{3}+12x^{2}-18x}{x}+\frac{\left(8x-12\right)x}{x}$$

Since \frac{g-2x^{3}+12x^{2}-18x}{x} and \frac{\left(8x-12\right)x}{x} have the same denominator, add them by adding their numerators.

$$\frac{g-2x^{3}+12x^{2}-18x+\left(8x-12\right)x}{x}$$

Do the multiplications in g-2x^{3}+12x^{2}-18x+\left(8x-12\right)x.

$$\frac{g-2x^{3}+12x^{2}-18x+8x^{2}-12x}{x}$$

Combine like terms in g-2x^{3}+12x^{2}-18x+8x^{2}-12x.

$$\frac{-2x^{3}+g+20x^{2}-30x}{x}$$