Answer
The real solutions to the equation $6x(x-1)=21-x$ are $x=\frac{-3}{2}$ and $x=\frac{7}{3}$
Work Step by Step
1. Distribute the $6x$: $6x^{2}-6x=21-x$
2. Add x to each side: $6x^{2}-5x=21$
3. Subtract 21 from each side: $6x^{2}-5x-21=0$
4. 1. Factor $6x^{2}-5x-21$. The factors are (-2x-3)(-3x+7) because $-2x\times-3x = 6x^{2}$(the a value in $a^{2}+bx+c$) and $-3\times7=-21$ the c value in the equation. When the factors are FOILED out, they equal the equation $6x^{2}-5x-21$.
5. Set both factors equal to zero: $-2x-3=0$ and $-3x+7=0$
6. Solve: $x=\frac{-3}{2}$ and $x=\frac{7}{3}$
