How do you solve quadratics? Factor, then set each factor equal to 0 and solve. To get 0 as an answer to a multiplication problem, one of the things multiplied must be a zero.

Solving Quadratic Equations Using Factoring

To solve the quadratic equation using factoring
1. Transform the equation using standard form in which one side is zero.
2. Factor the non-zero side.
3. Set each factor to zero (Remember: a product of factors is zero if and only if one or more of the factors is zero).
4. Solve each resulting equation.

Example 1:

• Solve the equation, x² – 3x – 10 = 0
• Factor the left side: (x – 5)(x + 2) = 0
• Set each factor to zero: x – 5 = 0 or x + 2 = 0
• Solve each equation: x = 5 or x = –2
• The solution set is {5, –2}.

Example 2:

• Solve the equation, 2x² + 5x = 12
• Set the right side to zero: 2x² + 5x – 12 = 0
• Factor the left side: (2x – 3)(x + 4) = 0
• Set each factor to zero: 2x – 3 = 0 or x + 4 = 0
• Solve each equation: x = 3/2 or x = –4

The solution set is {3/2, –4}
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