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Simplifying x2(4e2x) + 4x(2e2x) + -18(e2x) = 0 Remove parenthesis around (4e2x) x2 * 4e2x + 4x(2e2x) + -18(e2x) = 0 Reorder the terms for easier multiplication: 4x2 * e2x + 4x(2e2x) + -18(e2x) = 0 Multiply x2 * e2x 4e2x3 + 4x(2e2x) + -18(e2x) = 0 Remove parenthesis around (2e2x) 4e2x3 + 4x * 2e2x + -18(e2x) = 0 Reorder the terms for easier multiplication: 4e2x3 + 4 * 2x * e2x + -18(e2x) = 0 Multiply 4 * 2 4e2x3 + 8x * e2x + -18(e2x) = 0 Multiply x * e2x 4e2x3 + 8e2x2 + -18(e2x) = 0 Reorder the terms: -18e2x + 8e2x2 + 4e2x3 = 0 Solving -18e2x + 8e2x2 + 4e2x3 = 0 Solving for variable 'e'. Move all terms containing e to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '2e2x'. 2e2x(-9 + 4x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'e2x' equal to zero and attempt to solve: Simplifying e2x = 0 Solving e2x = 0 Move all terms containing e to the left, all other terms to the right. Simplifying e2x = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-9 + 4x + 2x2)' equal to zero and attempt to solve: Simplifying -9 + 4x + 2x2 = 0 Solving -9 + 4x + 2x2 = 0 Move all terms containing e to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 4x + 9 + 2x2 = 0 + 9 Reorder the terms: -9 + 9 + 4x + 2x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 4x + 2x2 = 0 + 9 4x + 2x2 = 0 + 9 Combine like terms: 0 + 9 = 9 4x + 2x2 = 9 Add '-4x' to each side of the equation. 4x + -4x + 2x2 = 9 + -4x Combine like terms: 4x + -4x = 0 0 + 2x2 = 9 + -4x 2x2 = 9 + -4x Add '-2x2' to each side of the equation. 2x2 + -2x2 = 9 + -4x + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 = 9 + -4x + -2x2 Simplifying 0 = 9 + -4x + -2x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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