3x^(2)+7x-6=0

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3x^(2)+7x-6=0

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Find the Factors: Step Title: Find the Factors Concise Step Description: Find two numbers that multiply to the product of the first and last coefficients (3 * -6 = -18) and add to the middle coefficient (7). Step Calculation: Factors of -18 that add up to 7 are 9 and -2 (because 9 * -2 = -18 and 9 + (-2) = 7). Step Output: Factors: 9, -2Write the Factored Form: Step Title: Write the Factored Form Concise Step Description: Write the factored form of the quadratic equation using the factors found in the previous step, and split the middle term accordingly. Step Calculation: The quadratic equation can be rewritten as 3x^2 + 9x - 2x - 6. Now, group the terms to factor by grouping: (3x^2 + 9x) + (-2x - 6). Step Output: Grouped terms: (3x^2 + 9x) and (-2x - 6)Factor by Grouping: Step Title: Factor by Grouping Concise Step Description: Factor out the greatest common factor from each group. Step Calculation: From the first group (3x^2 + 9x), factor out 3x to get 3x(x + 3). From the second group (-2x - 6), factor out -2 to get -2(x + 3). Step Output: Factored groups: 3x(x + 3) and -2(x + 3)Combine the Groups: Step Title: Combine the Groups Concise Step Description: Combine the factored groups to write the final factored form of the quadratic equation. Step Calculation: Since both groups contain the factor (x + 3), combine them to get (3x - 2)(x + 3). Step Output: Final factored form: (3x - 2)(x + 3)

$3 x^{2}+7 x-6=0$

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3x2+7x−6=0 3 x^{2}+7 x-6=0 3x2+7x−6=0

$3 x^{2}+7 x-6=0$