Question

Use the zero product property to find the solutions to the equation 6x^2- 5x = 56.

Answer 1

`\large\boxed{x=-(8)/(3)\ or\ x=(7)/(2)}`

Explanation:

`6x^2-5x=56\qquad\text{subtract 56 from both sides}\\\\6x^2-5x-56=0\\\\6x^2+16x-21x-56=0\\\\2x(3x+8)-7(3x+8)=0\\\\(3x+8)(2x-7)=0\iff 3x+8=0\ \vee\ 2x-7=0\\\\3x+8=0\qquad\text{subtract 8 from both sides}\\3x=-8\qquad\text{divide both sides by 3}\\\boxed{x=-(8)/(3)}\\\\2x-7=0\qquad\text{add 7 to both sides}\\2x=7\qquad\text{divide both sides by 2}\\\boxed{x=(7)/(2)}`