Determine a quadratic equation that you want to solve, and rearrange it into its standard form, which is ax^2 + bx + c = 0. In the standard form, "a," "b" and "c" represent the number portions of each term. For example, rearrange the quadratic equation x^2 + 5x = -6 into its standard form by adding 6 to both sides of the equation. This results in x^2 + 5x + 6 = 0, with a trinomial on the left side of the equation. A trinomial is an expression with three terms.
Factor the equation by finding the two expressions that equal the trinomial on the left side of the equation when multiplied together. Each factor expression will have two terms. Find the first terms of each factor expression by determining the factors that equal the first term of the trinomial when multiplied together. For example, x times x equals x^2. Therefore, x is the first term of each expression in the following form: (x )(x ).
Find the second terms of each factor expression by determining the two numbers that equal the number in the third term of the trinomial when multiplied together. These two terms must also equal the number in the trinomial's second term when added together. For example, the numbers 2 and 3 equal 6 when multiplied together, and equal 5 when added together. Therefore, 2 and 3 are the second terms of the factor expressions. This results in the factored equation (x + 2)(x + 3) = 0.
Set the first factor equal to 0. For example, x + 2 = 0.
Solve for the variable. For example, subtract 2 from both sides of the equation, which results in x + 2 - 2 = 0 - 2. This leaves x = -2, which is the first solution.
Set the second factor equal to 0. For example, x + 3 = 0.
Solve for the variable. For example, subtract 3 from both sides, which results in x + 3 - 3 = 0 - 3. This leaves x = -3, which is the second solution.
Write your results as a solution set with the first and second solutions separated by a comma and enclosed in brackets. For example, the solution set for the equation is {-2, -3}.