solve for the roots:4(2x²-3)=3x²-7x-12​

Step-by-step explanation:Here's how to solve for the roots of the equation: 1. Expand and Simplify: - Distribute the 4 on the left side: 8x² - 12 = 3x² - 7x - 12- Move all terms to one side: 8x² - 3x² + 7x - 12 + 12 = 0- Combine like terms: 5x² + 7x = 02. Factor out a Common Factor: - Notice that both terms have 'x' in common: x(5x + 7) = 03. Zero Product Property: - For the product of two factors to be zero, at least one of them must be zero. So, we have two possibilities:- x = 0- 5x + 7 = 04. Solve for x: - 5x + 7 = 0- Subtract 7 from both sides: 5x = -7- Divide both sides by 5: x = -7/5 Therefore, the roots of the equation are x = 0 and x = -7/5.

Answered by angeldenaga1 | 2024-09-10