solve quadratic equation by factoring

5x^2-6x-11=-3

5x^2-6x-11=-3

5x^2-6x-8=0

(5x + 4)(x - 2) = 0

take over please.

5x^2-6x-8=0

(5x-4)(x+2)=0

To solve a quadratic equation by factoring, you need to find two binomials whose product is equal to the quadratic equation.

Let's solve the given quadratic equation step by step:

1. Start by moving all the terms to one side of the equation, so the equation becomes:
5x^2 - 6x - 11 + 3 = 0

2. Simplify the equation:
5x^2 - 6x - 8 = 0

3. Look for factors of the coefficient of x^2 (5) and the constant term (-8) that combine to give the coefficient of x (-6). In this case, the factors are 4 and 2.
5x^2 + 4x - 2x - 8 = 0

4. Group the terms:
(5x^2 + 4x) - (2x + 8) = 0

5. Factor out the greatest common factor from each grouping:
x(5x + 4) - 2(5x + 4) = 0

6. Notice that (5x + 4) is a common factor in both terms:
(5x + 4)(x - 2) = 0

7. Set each factor equal to zero and solve for x:
5x + 4 = 0 or x - 2 = 0

For the first equation, subtract 4 from both sides and divide by 5 to solve for x:
5x = -4
x = -4/5

For the second equation, add 2 to both sides to solve for x:
x = 2

Therefore, the solutions to the quadratic equation 5x^2 - 6x - 11 = -3 are x = -4/5 and x = 2.