Factoring
When a is not 1
Example 1
Step 1. Multiply a and c.
In this equation, a = 2 and c = -6, therefore ac = -12.
In this equation ac = -12.
The factor pairs of -12 are 1 and -12, -1 and 12, 2 and -6, -2 and 6, 3 and -4, -3 and 4.
Step 3. Determine which factor pair has the sum of b.
In this equation b = 1.
The sum of the factor pairs are 1 + -12 = -11, -1 + 12 = 11, 2 + -6 = -4, -2 + 6 = 4, 3 + -4 = -1, -3 + 4 = 1.
4 and -3 have the correct sum.
Step 4. Substitute the roots into the original equation in place of b.
2x2 + (4 + -3)x - 6 = 0
2x2 + 4x + -3x - 6 = 0
Step 5. Factor by grouping the first two terms and the last two terms together and find their GCF.
(2x2 + 4x) + (-3x - 6) = 0
2x(x + 2) -3(x + 2) = 0
(x + 2)(2x - 3) = 0
Step 6. Use the Zero Product Property to set each factor equal to zero and solve.
x + 2 = 0 or 2x - 3 = 0