((2x+3)*(4x²-3x+7))

To multiply the expression (2x+3) by (4x^2-3x+7), we can use the distributive property.

Step 1: Multiply 2x by each term in (4x^2-3x+7) 2x * 4x^2 = 8x^3 2x * -3x = -6x^2 2x * 7 = 14x

Step 2: Multiply 3 by each term in (4x^2-3x+7) 3 * 4x^2 = 12x^2 3 * -3x = -9x 3 * 7 = 21

Step 3: Combine like terms The result of multiplying (2x+3) by (4x^2-3x+7) is: 8x^3 - 6x^2 + 14x + 12x^2 - 9x + 21

Simplifying the terms: 8x^3 + (12x^2 - 6x^2) + (14x - 9x) + 21

Finally, the expression simplifies to: 8x^3 + 6x^2 + 5x + 21