Final answer:
To solve the equation algebraically, group like terms, set the equation equal to zero, factor, and solve for x.
Step-by-step explanation:
To solve the equation 2x^2 + 5x - 3 = x^2 + 4x + 3 algebraically, we need to collect like terms and set the equation equal to zero.
Grouping like terms, we get x^2 + (4x - 5x) + (3 - 3) = 0.
This simplifies to x^2 - x = 0.
Factoring out an x, we have x(x - 1) = 0.
Setting each factor equal to zero, we find two possible solutions: x = 0 and x = 1. These are the values that satisfy the original equation.