Example 2

Solve by factoring and then verify the solution.

Rearrange the equation so one side of the equal sign is zero.

Factor the quadratic expression.

12m2 - 5m - 3 = 0
Product of 12(-3) = -36, Sum of -5

The two numbers are -9 and 4.
Decompose the middle term, group, and factor.

12m2 - 9m + 4m - 3 = 0
(12m2 - 9m) + (4m - 3) = 0
3m(4m - 3) + 1(4m - 3) = 0
(4m - 3)(3m + 1) = 0

Determine what value of the variable makes each factor equal to zero.

The solutions are and . Verify the solutions by substituting them into the original equation.

For m = ,

Left side
Right side
3
LS = RS

The two sides are equal, so is a solution.

For m = ,

Left side
Right side
3
LS = RS

The two sides are equal, so is a solution.