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Solve for x. Enter the solutions from least to greatest. {:[6x^(2)-6x-72=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newline6x2−6x−72=0 6 x^{2}-6 x-72=0 \newlinelesser x= x= \newlinegreater x= x=

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Q. Solve for x x . Enter the solutions from least to greatest.\newline6x2−6x−72=0 6 x^{2}-6 x-72=0 \newlinelesser x= x= \newlinegreater x= x=
  1. Simplify the equation: Simplify the equation if possible.\newlineThe equation is 6x2−6x−72=06x^2 - 6x - 72 = 0. We can simplify this equation by factoring out the greatest common factor, which is 66.\newline6(x2−x−12)=06(x^2 - x - 12) = 0
  2. Solve the factored equation: Solve the factored equation.\newlineNow we have 6(x2−x−12)=06(x^2 - x - 12) = 0. We can set the expression inside the parentheses equal to zero because if the product is zero, one of the factors must be zero.\newlinex2−x−12=0x^2 - x - 12 = 0
  3. Factor the quadratic equation: Factor the quadratic equation.\newlineWe need to find two numbers that multiply to −12-12 and add up to −1-1 (the coefficient of xx). These numbers are −4-4 and 33.\newline(x−4)(x+3)=0(x - 4)(x + 3) = 0
  4. Solve for x: Solve for x.\newlineSet each factor equal to zero and solve for x.\newlinex−4=0x - 4 = 0 or x+3=0x + 3 = 0\newlinex=4x = 4 or x=−3x = -3
  5. Order the solutions: Order the solutions from least to greatest.\newlineThe lesser value of xx is −3-3, and the greater value of xx is 44.

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