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Simplifying 0 = 2x3 + 3x2 + -252x Reorder the terms: 0 = -252x + 3x2 + 2x3 Solving 0 = -252x + 3x2 + 2x3 Solving for variable 'x'. Remove the zero: 252x + -3x2 + -2x3 = -252x + 3x2 + 2x3 + 252x + -3x2 + -2x3 Reorder the terms: 252x + -3x2 + -2x3 = -252x + 252x + 3x2 + -3x2 + 2x3 + -2x3 Combine like terms: -252x + 252x = 0 252x + -3x2 + -2x3 = 0 + 3x2 + -3x2 + 2x3 + -2x3 252x + -3x2 + -2x3 = 3x2 + -3x2 + 2x3 + -2x3 Combine like terms: 3x2 + -3x2 = 0 252x + -3x2 + -2x3 = 0 + 2x3 + -2x3 252x + -3x2 + -2x3 = 2x3 + -2x3 Combine like terms: 2x3 + -2x3 = 0 252x + -3x2 + -2x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(252 + -3x + -2x2) = 0 Factor a trinomial. x((21 + -2x)(12 + x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(21 + -2x)' equal to zero and attempt to solve: Simplifying 21 + -2x = 0 Solving 21 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + -2x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -2x = 0 + -21 -2x = 0 + -21 Combine like terms: 0 + -21 = -21 -2x = -21 Divide each side by '-2'. x = 10.5 Simplifying x = 10.5Subproblem 3
Set the factor '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Simplifying x = -12Solution
x = {0, 10.5, -12}
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