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Simplifying 2x3 + 6x2 + 12x2 = 4x3 + 16x2 Reorder the terms: 6x2 + 12x2 + 2x3 = 4x3 + 16x2 Combine like terms: 6x2 + 12x2 = 18x2 18x2 + 2x3 = 4x3 + 16x2 Reorder the terms: 18x2 + 2x3 = 16x2 + 4x3 Solving 18x2 + 2x3 = 16x2 + 4x3 Solving for variable 'x'. Reorder the terms: 18x2 + -16x2 + 2x3 + -4x3 = 16x2 + 4x3 + -16x2 + -4x3 Combine like terms: 18x2 + -16x2 = 2x2 2x2 + 2x3 + -4x3 = 16x2 + 4x3 + -16x2 + -4x3 Combine like terms: 2x3 + -4x3 = -2x3 2x2 + -2x3 = 16x2 + 4x3 + -16x2 + -4x3 Reorder the terms: 2x2 + -2x3 = 16x2 + -16x2 + 4x3 + -4x3 Combine like terms: 16x2 + -16x2 = 0 2x2 + -2x3 = 0 + 4x3 + -4x3 2x2 + -2x3 = 4x3 + -4x3 Combine like terms: 4x3 + -4x3 = 0 2x2 + -2x3 = 0 Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(1 + -1x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0, 1}
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