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Simplifying 7 = x3 + 2x2 + -48x + 7 Reorder the terms: 7 = 7 + -48x + 2x2 + x3 Add '-7' to each side of the equation. 7 + -7 = 7 + -48x + 2x2 + -7 + x3 Combine like terms: 7 + -7 = 0 0 = 7 + -48x + 2x2 + -7 + x3 Reorder the terms: 0 = 7 + -7 + -48x + 2x2 + x3 Combine like terms: 7 + -7 = 0 0 = 0 + -48x + 2x2 + x3 0 = -48x + 2x2 + x3 Solving 0 = -48x + 2x2 + x3 Solving for variable 'x'. Remove the zero: 48x + -2x2 + -1x3 = -48x + 2x2 + x3 + 48x + -2x2 + -1x3 Reorder the terms: 48x + -2x2 + -1x3 = -48x + 48x + 2x2 + -2x2 + x3 + -1x3 Combine like terms: -48x + 48x = 0 48x + -2x2 + -1x3 = 0 + 2x2 + -2x2 + x3 + -1x3 48x + -2x2 + -1x3 = 2x2 + -2x2 + x3 + -1x3 Combine like terms: 2x2 + -2x2 = 0 48x + -2x2 + -1x3 = 0 + x3 + -1x3 48x + -2x2 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 48x + -2x2 + -1x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(48 + -2x + -1x2) = 0 Factor a trinomial. x((6 + -1x)(8 + 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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Subproblem 3
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Solution
x = {0, 6, -8}
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