solve by factoring: 2h^2-h-3=0

(2h-3)(h+1) = 0

I factored it, now you solve it.

then h=3/2 v h=-1

To solve the given quadratic equation by factoring, we need to find two binomials whose product equals the quadratic equation.

The equation we need to solve is:

2h^2 - h - 3 = 0

Step 1: Multiply the coefficient of the quadratic term (2) with the constant term (-3). In this case, 2 × -3 = -6.

Step 2: Find two numbers whose product is -6 and whose sum is the coefficient of the linear term (-1). The numbers -3 and 2 satisfy these conditions since -3 × 2 = -6 and -3 + 2 = -1.

Step 3: Split the linear term (-h) into two terms using the numbers found in step 2:

2h^2 - h - 3 = 0
2h^2 - 3h + 2h - 3 = 0

Step 4: Group the terms:

(2h^2 - 3h) + (2h - 3) = 0

Step 5: Factor out the greatest common factor from both groups:

h(2h - 3) + 1(2h - 3) = 0

Step 6: Notice that we have a common binomial in both terms (2h - 3).

(2h - 3)(h + 1) = 0

Now we have factored the quadratic equation as the product of two binomials.

Step 7: Set each factor equal to zero and solve for 'h':

2h - 3 = 0 or h + 1 = 0

Solving these equations:

For 2h - 3 = 0:
2h = 3
h = 3/2

For h + 1 = 0:
h = -1

Therefore, the solutions to the quadratic equation 2h^2 - h - 3 = 0 are h = 3/2 and h = -1.