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Solve 3x^2 + 7x - 6 = 0

Worked through step by step. More quadratics.

Answer
x=23,−3\boxed{x = \frac{2}{3}, -3}

Substituting these values back into the original equation yields 00, confirming they are the correct roots.

Problem: Solve the quadratic equation 3x2+7x−6=03x^2 + 7x - 6 = 0.

Steps

  1. Factor by grouping
    3x2+9x−2x−6=03x^2 + 9x - 2x - 6 = 0
  2. Group terms
    3x(x+3)−2(x+3)=03x(x + 3) - 2(x + 3) = 0
  3. Factor out the common binomial
    (3x−2)(x+3)=0(3x - 2)(x + 3) = 0
  4. Set each factor to zero
    3x−2=0orx+3=03x - 2 = 0 \quad \text{or} \quad x + 3 = 0
  5. Solve the linear equations
    x=23orx=−3x = \frac{2}{3} \quad \text{or} \quad x = -3

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