Solve the equation for all real solutions in simplest form.2, a, squared, plus, 4, a, minus, 6, equals, minus, 3, a2a 2 +4a−6=−3a

The equation you've provided seems to have a typo. I believe it should be "2a^2 + 4a - 6 = -3a". Let's solve this equation step by step:

Step 1: Rearrange the equation to set it equal to zero. This gives us:

2a^2 + 4a + 3a - 6 = 0

Step 2: Combine like terms:

2a^2 + 7a - 6 = 0

Step 3: Now, we need to factor the quadratic equation. We're looking for two numbers that multiply to (2*-6)=-12 and add to 7. Those numbers are 4 and -3. So, we can write the equation as:

2a^2 + 4a + 3a - 6 = 0

2a(a + 2) + 3(a + 2) = 0

Step 4: Now, we can factor out (a + 2):

(a + 2)(2a + 3) = 0

Step 5: Finally, we set each factor equal to zero and solve for a:

a + 2 = 0 => a = -2

2a + 3 = 0 => a = -3/2

So, the solutions to the equation are a = -2 and a = -3/2.