Solve the quadratic by factoring.4, x, squared, minus, 16, x, plus, 12, equals, minus, 9, x, plus, 94x 2 −16x+12=−9x+9

First, let's simplify the equation by moving all terms to one side.

4x^2 - 16x + 12 = -9x + 9

This simplifies to:

4x^2 - 16x + 9x + 12 - 9 = 0

Which further simplifies to:

4x^2 - 7x + 3 = 0

Now, let's factor the quadratic equation. We're looking for two numbers that multiply to (4*3)=12 and add up to -7. Those numbers are -4 and -3.

So, we can rewrite -7x as -4x - 3x:

4x^2 - 4x - 3x + 3 = 0

Now, group the terms two at a time:

4x(x - 1) - 3(x - 1) = 0

Now, you can see that (x - 1) is a common factor:

(4x - 3)(x - 1) = 0

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

4x - 3 = 0 => x = 3/4

x - 1 = 0 => x = 1

So, the solutions to the equation 4x^2 - 16x + 12 = -9x + 9 are x = 3/4 and x = 1.