3x^2+11x-20=0
(3x -4)(x + 5) = 0
x = 4/3 or -5
To solve the quadratic equation 3x^2 + 11x - 20 = 0, we can use the factoring method.
Step 1: Look for two numbers that multiply to give you -20 and add up to give you 11. In this case, those numbers are 15 and -4.
Step 2: Rewrite the middle term (11x) using those two numbers: 3x^2 + 15x - 4x - 20 = 0.
Step 3: Group the terms: (3x^2 + 15x) + (-4x - 20) = 0.
Step 4: Factor out the greatest common factor from each group: 3x(x + 5) - 4(x + 5) = 0.
Step 5: Notice that both groups have a common factor of (x + 5), so we can factor it out: (3x - 4)(x + 5) = 0.
Now we have two binomial factors that, when multiplied, give us zero.
Step 6: To find the values of x, set each factor equal to zero and solve for x:
3x - 4 = 0 gives x = 4/3 (4 divided by 3),
and
x + 5 = 0 gives x = -5.
Therefore, the solutions to the equation 3x^2 + 11x - 20 = 0 are x = 4/3 or x = -5.