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Solve the quadratic by factoring.

4x^(2)-3x+12=5x+9
Answer: 
x=

Solve the quadratic by factoring.\newline4x23x+12=5x+9 4 x^{2}-3 x+12=5 x+9 \newlineAnswer: x= x=

Full solution

Q. Solve the quadratic by factoring.\newline4x23x+12=5x+9 4 x^{2}-3 x+12=5 x+9 \newlineAnswer: x= x=
  1. Move to Standard Form: Write the equation in standard form by moving all terms to one side of the equation.\newlineSubtract 5x5x and 99 from both sides of the equation 4x23x+12=5x+94x^2 - 3x + 12 = 5x + 9.\newline4x23x+125x9=04x^2 - 3x + 12 - 5x - 9 = 0\newlineCombine like terms.\newline4x28x+3=04x^2 - 8x + 3 = 0
  2. Identify Coefficients: Identify aa, bb, and cc in the standard form of the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0.\newlineFrom 4x28x+3=04x^2 - 8x + 3 = 0, we have:\newlinea=4a = 4\newlineb=8b = -8\newlinec=3c = 3
  3. Find Multiplying Numbers: Find two numbers that multiply to aca*c (43=124*3=12) and add up to bb (8-8).\newlineWe need to find two numbers that multiply to 1212 and add up to 8-8.\newlineHowever, there are no two such integers that satisfy both conditions. This means the quadratic cannot be factored using integers.
  4. Conclusion: Since the quadratic cannot be factored using integers, we can conclude that the quadratic equation does not have a solution that can be expressed as a factoring of integers. We may need to use other methods such as completing the square or the quadratic formula to find the solutions.