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Solve for the Value of S (2S+2) (3S-2)

Solve for the Value of S (2S+2) (3S-2)-example-1

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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.

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