Solve the equation for all real solutions in simplest form.4, m, squared, minus, m, minus, 3, equals, minus, m, squared4m 2 −m−3=−m 2

To solve the equation 4m^2 - m - 3 = -m^2, we can follow these steps:

Step 1: Combine like terms on both sides of the equation. 4m^2 + m^2 - m + m - 3 = 0

Step 2: Simplify the equation. 5m^2 - 3 = 0

Step 3: Move the constant term to the other side of the equation. 5m^2 = 3

Step 4: Divide both sides of the equation by 5 to isolate m^2. m^2 = 3/5

Step 5: Take the square root of both sides of the equation to solve for m. m = ±√(3/5)

Therefore, the real solutions in simplest form are m = √(3/5) and m = -√(3/5).