Upstudy AI Solution
Answer
Solution
Answered by UpStudy AI and reviewed by a Professional Tutor


The Deep Dive
To factor the equation \( 31x = 12x^2 + 20 \), first, move all terms to one side to set the equation to zero: \( 12x^2 - 31x + 20 = 0 \). Now, look for two numbers that multiply to \( 12 \times 20 = 240 \) and add up to \( -31 \). Those numbers are \( -16 \) and \( -15 \). Rewrite the equation using these numbers: \( 12x^2 - 16x - 15x + 20 = 0 \). Now group the terms: \( 4x(3x - 4) - 5(3x - 4) = 0 \). Factor by grouping: \( (3x - 4)(4x - 5) = 0 \). Thus, the factored form is \( (3x - 4)(4x - 5) = 0 \). You can solve for \( x \) by setting each factor to zero: \( 3x - 4 = 0 \) results in \( x = \frac{4}{3} \) and \( 4x - 5 = 0 \) results in \( x = \frac{5}{4} \). Happy factoring!