To solve for the value of S in the expression (2S+2)(3S-2), we can use the distributive property and simplify the expression.
1. Expand the expression using the distributive property:
(2S+2)(3S-2) = 2S * 3S + 2S * (-2) + 2 * 3S + 2 * (-2)
= 6S^2 - 4S + 6S - 4
2. Combine like terms:
The terms -4S and 6S can be combined since they have the same variable, S:
6S^2 - 4S + 6S - 4 = 6S^2 + 2S - 4
3. The expression is now in standard quadratic form. To solve for the value of S, we set the expression equal to zero and factorize it:
6S^2 + 2S - 4 = 0
4. Factorize the quadratic expression:
To factorize the quadratic expression, we look for two numbers that multiply to give -24 (the product of 6 and -4) and add up to 2. The numbers that satisfy these conditions are 6 and -4:
6S^2 + 2S - 4 = (2S - 2)(3S + 2)
5. Set each factor equal to zero and solve for S:
2S - 2 = 0 or 3S + 2 = 0
6. Solve for S in each equation:
2S - 2 = 0 -> 2S = 2 -> S = 1
3S + 2 = 0 -> 3S = -2 -> S = -2/3
Therefore, the value of S in the expression (2S+2)(3S-2) is S = 1 or S = -2/3.