(x – 10)(x – 2) = -20

Rearrange that equation so there is zero on one side

x^2 -12x +20 = -20
x^2 -12x +40 = 0
Use the quadratic equation to solve that.
One root is
x = [12 + sqrt(-16)]/2
= 6 + 2i

6r · s · 4rt

To solve the given equation (x - 10)(x - 2) = -20, we can follow these steps:

Step 1: Distribute the terms on the left side of the equation:
(x - 10)(x - 2) = -20
x(x - 2) - 10(x - 2) = -20
x^2 - 2x - 10x + 20 = -20
x^2 - 12x + 20 = -20

Step 2: Simplify the equation by combining like terms:
x^2 - 12x + 20 + 20 = 0
x^2 - 12x + 40 = 0

Step 3: Set the equation equal to zero, as we want to find the values of x that make the equation true.

Step 4: We have a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = -12, and c = 40.

Step 5: To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. In this case, factoring may not be straightforward, so let's use the quadratic formula:

The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values a = 1, b = -12, and c = 40 into the quadratic formula, we have:
x = (-(-12) ± √((-12)^2 - 4(1)(40))) / (2(1))
x = (12 ± √(144 - 160)) / 2
x = (12 ± √(-16)) / 2

Step 6: Notice that we have a square root of a negative number, which means that the equation has no real solutions. The expression √(-16) is imaginary, and since we cannot take the square root of a negative number in the real number system, there are no real values of x that satisfy the equation.

Therefore, the given equation (x - 10)(x - 2) = -20 has no solutions.