1. **State the problem:** Simplify or analyze the quadratic expression $5x^2 + 6x - 8$. 2. **Recall the quadratic form:** A quadratic expression is generally written as $ax^2 + bx + c$ where $a$, $b$, and $c$ are constants. 3. **Identify coefficients:** Here, $a=5$, $b=6$, and $c=-8$. 4. **Factor the quadratic (if possible):** We look for two numbers that multiply to $a \times c = 5 \times (-8) = -40$ and add to $b=6$. 5. The pair of numbers that satisfy this are $10$ and $-4$ because $10 \times (-4) = -40$ and $10 + (-4) = 6$. 6. Rewrite the middle term using these numbers: $$5x^2 + 10x - 4x - 8$$ 7. Group terms: $$ (5x^2 + 10x) + (-4x - 8) $$ 8. Factor each group: $$ 5x(x + 2) - 4(x + 2) $$ 9. Factor out the common binomial: $$ (5x - 4)(x + 2) $$ 10. **Final answer:** The factorization of $5x^2 + 6x - 8$ is $$ (5x - 4)(x + 2) $$.