Solve by Factoring x^2-7x+12=0

Problem

x2−7*x+12=0

Solution

1. Identify the coefficients of the quadratic equation in the form a*x2+b*x+c=0 where a=1 b=−7 and c=12

2. Find two numbers that multiply to c (12 and add to b (−7.

3. Determine that the two numbers are −3 and −4 because (−3)*(−4)=12 and −3+(−4)=−7

4. Rewrite the quadratic expression as a product of two binomials using these numbers.

(x−3)*(x−4)=0

5. Apply the zero product property by setting each factor equal to zero.

x−3=0

x−4=0

6. Solve each linear equation for x

x=3

x=4

Final Answer

x2−7*x+12=0⇒x=3,4

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