Certainly! Let's solve the given mathematical expression step-by-step:
[tex]\[(90 \div 6) \times [-5 + [-4(3-8) - (12-3) + 4]]\][/tex]
1. Divide 90 by 6:
[tex]\[90 \div 6 = 15\][/tex]
2. Evaluate the inner expression inside the brackets:
a. First, simplify the term inside the parentheses:
[tex]\[
3 - 8 = -5
\][/tex]
b. Next, multiply -4 by the result of the previous step:
[tex]\[
-4 \times (-5) = 20
\][/tex]
c. Now, simplify the term (12-3):
[tex]\[
12 - 3 = 9
\][/tex]
d. Make the term - (12-3) negative:
[tex]\[
-(12 - 3) = -9
\][/tex]
e. Combine all parts of the inner expression:
[tex]\[
20 + (-9) + 4
\][/tex]
f. Add these results together:
[tex]\[
20 - 9 + 4 = 15
\][/tex]
3. Combine the result with -5:
[tex]\[
-5 + 15 = 10
\][/tex]
4. Finally, multiply the result of the division by the result of the expression:
[tex]\[
15 \times 10 = 150
\][/tex]
So, the value of the given expression is:
[tex]\[
150
\][/tex]
