Write an equation in which the quadratic expression 2c^2 - 2x - 12 equals 0. Show the expression in factores form and explain what your solutions mean for the equation. Show your work.

1. (2x + 4)(x - 3) = 0

2. The solutions to the expression are

-2 and 3.

Step-by-step explanation:

1. The expression 2x² - 2x - 12 = 0

can be expressed in factor form as follow:

2x² - 2x - 12 = 0

Multiply the first term i.e 2x² and the last term i.e -12 together. We have:

2x² × -12 = -24x²

Next, look for two factors of -24x² such that their sum will result to the 2nd term i.e -2x in the expression above. The two factors are -6x and 4x.

Next, substitute -6x and 4x in place of -2x in the expression above i.e

2x² - 2x - 12 = 0

2x² - 6x + 4x - 12 = 0

Next, we shall factorize

2x(x - 3) + 4(x - 3) = 0

(2x + 4)(x - 3) = 0

2. The solution to expression

(2x + 4)(x - 3) = 0

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

Collect like terms

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

2x = - 4 or x = 3

x = - 4/2 or x = 3

x = - 2 or 3

Therefore, the solutions to the expression are - 2 and 3.