Solve H=(3x+4)(x-5)-(3x+4)

$$H = ( 3 x + 4 ) ( x - 5 ) - ( 3 x + 4 )$$

Solve for H

$$H=\left(x-6\right)\left(3x+4\right)$$

Solution Steps

Use the distributive property to multiply 3x+4 by x-5 and combine like terms.

$$H=3x^{2}-11x-20-\left(3x+4\right)$$

To find the opposite of 3x+4, find the opposite of each term.

$$H=3x^{2}-11x-20-3x-4$$

Combine -11x and -3x to get -14x.

$$H=3x^{2}-14x-20-4$$

Subtract 4 from -20 to get -24.

$$H=3x^{2}-14x-24$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{3H+121}+7}{3}$$

$$x=\frac{\sqrt{3H+121}+7}{3}$$

Solve for x

$$x=\frac{-\sqrt{3H+121}+7}{3}$$

$$x=\frac{\sqrt{3H+121}+7}{3}\text{, }H\geq -\frac{121}{3}$$