tting the input :Changes made to your input should not affect the solution: (1): "x2" was replaced by "x^2". Step by step solution :STEP1:Equation at the end of step 1 ((2•3x2) - 24x) + 18 = 0 STEP2:STEP3:Pulling out like terms 3.1 Pull out like factors : 6x2 - 24x + 18 = 6 • (x2 - 4x + 3) Trying to factor by splitting the middle term 3.2 Factoring x2 - 4x + 3 The first term is, x2 its coefficient is 1 .The middle term is, -4x its coefficient is -4 .The last term, "the constant", is +3 Step-1 : Multiply the coefficient of the first term by the constant 1 • 3 = 3 Step-2 : FIND two factors of 3 whose sum equals the coefficient of the middle term, which is -4 . -3 + -1 = -4 That's itStep-3 : Rewrite the polynomial splitting the middle term using the two factors FOUND in step 2 above, -3 and -1 x2 - 3x - 1x - 3Step-4 : Add up the first 2 terms, pulling out like factors : x • (x-3) Add up the last 2 terms, pulling out common factors : 1 • (x-3)Step-5 : Add up the four terms of step 4 : (x-1) • (x-3) Which is the desired factorizationEquation at the end of step3: 6 • (x - 1) • (x - 3) = 0 STEP4:Theory - Roots of a product 4.1 A product of several terms equals zero. When a product of two or more terms equals zero, then at least one of the terms MUST be zero. We shall now solve each term = 0 separately In other words, we are going to solve as MANY equations as there are terms in the product Any solution of term = 0 solves product = 0 as well.Equations which are never TRUE: 4.2 Solve : 6 = 0This equation has no solution.A a non-zero constant never equals zero.Solving a Single Variable Equation: 4.3 Solve : x-1 = 0 Add 1 to both sides of the equation : x = 1Solving a Single Variable Equation: 4.4 Solve : x-3 = 0 Add 3 to both sides of the equation : x = 3Supplement : Solving Quadratic Equation DirectlySolving x2-4x+3 = 0 directly Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic FormulaParabola, Finding the Vertex: 5.1 Find the Vertex of y = x2-4x+3Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).