Answer: The number of solutions to the given equation is zero.
Step-by-step explanation: We are given to find the number of solutions to the following equation :
[tex]-4(5-3x)=12x+20~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the number of solutions, we must solve the given equation.
The solution of equation (i) is as follows :
[tex]-4(5-3x)=12x+20\\\\\Rightarrow 5-3x=\dfrac{12x+20}{-4}\\\\\Rightarrow 5-3x=-3x-5\\\\\Rightarrow -3x+3x=-5-5\\\\\Rightarrow 0=-10,[/tex] which can never be possible.
So, the given equation has no solution.
Thus, the number of solutions to the given equation is zero.
