Problem:
Find the sum of 4(3x) and -4x + 2x, subtracted from the sum of 3x^2 - 5x and -x^2 + 2x + 5.

Solution:

To find the sum of the given expressions, we need to simplify each expression separately and then perform the necessary operations.

Simplifying the Expressions:

Let's simplify each expression step by step:

1. Simplifying the expression 4(3x):
- Multiply 4 and 3x: 4 * 3x = 12x

Therefore, the simplified expression is 12x.

2. Simplifying the expression -4x + 2x:
- Combine like terms: -4x + 2x = -2x

Therefore, the simplified expression is -2x.

3. Simplifying the expression 3x^2 - 5x:
- No further simplification can be done.

Therefore, the simplified expression is 3x^2 - 5x.

4. Simplifying the expression -x^2 + 2x + 5:
- No further simplification can be done.

Therefore, the simplified expression is -x^2 + 2x + 5.

Performing the Operations:

Now that we have simplified each expression, let's perform the necessary operations to find the sum:

1. Sum of 4(3x) and -4x + 2x:
- We have already simplified these expressions as 12x and -2x.
- Sum of 12x and -2x: 12x + (-2x) = 12x - 2x = 10x

Therefore, the sum of 4(3x) and -4x + 2x is 10x.

2. Sum of 3x^2 - 5x and -x^2 + 2x + 5:
- We have already simplified these expressions as 3x^2 - 5x and -x^2 + 2x + 5.
- Sum of 3x^2 - 5x and -x^2 + 2x + 5: (3x^2 - 5x) + (-x^2 + 2x + 5)
- Combine the like terms: 3x^2 - x^2 - 5x + 2x + 5 = 2x^2 - 3x + 5

Therefore, the sum of 3x^2 - 5x and -x^2 + 2x + 5 is 2x^2 - 3x + 5.

Subtracting the Sum:

Now, we subtract the sum of 10x from the sum of 2x^2 - 3x + 5:

Sum of 2x^2 - 3x + 5 minus 10x: (2x^2 - 3x + 5) - 10x
- Distribute the negative sign: 2x^2 - 3x + 5 - 10x
- Combine the like terms: 2x^2 - 3