Could we use multiple regression if the data do not shown the linearity? I have a problem with my research, 
actually i want to  use multiple regression to analyze my research, but i have problem.
1. Assumptions not fulfilled (normality and nonhomogeneous) 
2. The plots are not linear

What should i do with this problem?
could I use multiple regression or another statistic analysis?
 A: For ordinary least squares to provide the maximum likelihood estimate we have some fairly stringent conditions. Basically, we require the underlying model to be correctly specified and the errors must be normally distributed with mean zero and constant variance. If the errors have a non-constant variance, i.e. homoskedastic, then we can use weighted least squares.
Outside of those conditions, least squares estimators do not provide the maximum likelihood estimate. But, linear regression still provides an estimate, which may be better than nothing. But you should be aware that at the very least you can not rely on the standard error estimates or p-values when the underlying assumptions are violated.
So, what should you do? That depends in part on what you want to do. Are you using regression to explain or predict? An explanatory model should be based on some theoretical knowledge of the process you're modelling and a model of the measurement errors. 
But, since you're asking about applying linear regression to nonlinear data, it's safe to assume you're trying to predict future observations by training a model on a data set. In this case, you can do whatever you want. You could try multiple linear regression, polynomial regression, kernel regression, and more. The only relevant question is does it work? One way to answer the last question is 10-fold cross validation.
