Solve the equation $8 ( 6 - x ) - 3 x ( 6 - x ) = 0$ by factoring.
A) $\frac { 8 } { 3 } , 6$
B) $- \frac { 8 } { 3 } , - 6$
C) $\frac { 8 } { 3 } , 48$
D) $\frac { 3 } { 8 } , 6$
E) $- \frac { 3 } { 8 } , - 48$

Question

Quizplus · Accepted Answer

First, distribute the terms: $48 - 8x - 18x + 3x^2 = 0$, which simplifies to $3x^2 - 26x + 48 = 0$. Factoring this quadratic equation, we get $3x^2 - 18x - 8x + 48 = 0$, which can be grouped and factored further into $3x(x - 6) - 8(x - 6) = 0$. This gives us $(3x - 8)(x - 6) = 0$, leading to the solutions $x = \frac{8}{3}$ and $x = 6$.

Solve the Equation 8(6−x)−3x(6−x)=08 ( 6 - x ) - 3 x ( 6 - x ) = 08(6−x)−3x(6−x)=0

Solve the Equation $8 ( 6 - x ) - 3 x ( 6 - x ) = 0$