To solve the equation by factoring, we want to find two numbers that multiply to give the constant term (in this case -72) and add up to give the coefficient of the middle term (in this case 9).
The two numbers that satisfy these conditions are 12 and -6.
Therefore, we rewrite the equation as:
5x^2 + 12x - 6x - 72 = 0.
Now we factor by grouping:
(5x^2 + 12x) - (6x + 72) = 0
x(5x + 12) - 6(5x + 12) = 0
(x - 6)(5x + 12) = 0
Now we can set each factor equal to zero and solve for x:
x - 6 = 0 or 5x + 12 = 0
x = 6 or 5x = -12
x = -12/5
So the solutions to the equation are x = 6 and x = -12/5.
Solve the equation by factoring.
5x^2+9x-72=0
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