Sure, let's solve this step by step.
Step 1: It's given that the roots of the quadratic equation are x = -3 and x = 5. We'll take these two roots to construct our quadratic equation.
Step 2: The standard form of a quadratic equation is ax^2 + bx + c = 0, and the root form of a quadratic equation is (x - root1)(x - root2) = 0. Here, root1 and root2 are the roots of the equation.
Step 3: Substituting the given roots into the root form, we can get our quadratic equation. So, we replace root1 with -3 and root2 with 5. The root form of the equation becomes: (x - (-3))(x - 5) = 0.
Step 4: Simplify it, we get: (x + 3)(x - 5) = 0.
Step 5: Expand the left side of the equation using the distributive property (a(b + c) = ab + ac), we get: x^2 - 5x + 3x - 15 = 0,
Step 6: Further simplifying it by combining like terms, we get: x^2 - 2x - 15 = 0.
So, the standard form quadratic equation that has roots of both x=-3 and x=5 is x^2 - 2x - 15 = 0.