Solve the quadratic by factoring.5, x, squared, plus, 9, x, minus, 6, equals, 10, x5x 2 +9x−6=10x

First, let's rewrite the equation to bring all terms to one side:

5x^2 + 9x - 6 - 10x = 0

This simplifies to:

5x^2 - x - 6 = 0

Next, we factor the quadratic equation. We are looking for two numbers that multiply to -30 (5*-6) and add to -1. Those numbers are -6 and 5.

So, we can rewrite the equation as:

5x^2 - 6x + 5x - 6 = 0

Then, we group the terms and factor by grouping:

x(5x - 6) + 1(5x - 6) = 0

This gives us:

(5x - 6)(x + 1) = 0

Setting each factor equal to zero gives the solutions to the equation:

5x - 6 = 0 --> 5x = 6 --> x = 6/5

and

x + 1 = 0 --> x = -1

So, the solutions to the equation 5x^2 + 9x - 6 = 10x are x = 6/5 and x = -1.