18x^7=81x^8+x^6

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Solution for 18x^7=81x^8+x^6 equation:


Simplifying
18x7 = 81x8 + x6

Reorder the terms:
18x7 = x6 + 81x8

Solving
18x7 = x6 + 81x8

Solving for variable 'x'.

Reorder the terms:
-1x6 + 18x7 + -81x8 = x6 + 81x8 + -1x6 + -81x8

Reorder the terms:
-1x6 + 18x7 + -81x8 = x6 + -1x6 + 81x8 + -81x8

Combine like terms: x6 + -1x6 = 0
-1x6 + 18x7 + -81x8 = 0 + 81x8 + -81x8
-1x6 + 18x7 + -81x8 = 81x8 + -81x8

Combine like terms: 81x8 + -81x8 = 0
-1x6 + 18x7 + -81x8 = 0

Factor out the Greatest Common Factor (GCF), 'x6'.
x6(-1 + 18x + -81x2) = 0

Factor a trinomial.
x6((-1 + 9x)(1 + -9x)) = 0

Subproblem 1

Set the factor 'x6' equal to zero and attempt to solve: Simplifying x6 = 0 Solving x6 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x6 = 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 '(-1 + 9x)' equal to zero and attempt to solve: Simplifying -1 + 9x = 0 Solving -1 + 9x = 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 + 9x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 9x = 0 + 1 9x = 0 + 1 Combine like terms: 0 + 1 = 1 9x = 1 Divide each side by '9'. x = 0.1111111111 Simplifying x = 0.1111111111

Subproblem 3

Set the factor '(1 + -9x)' equal to zero and attempt to solve: Simplifying 1 + -9x = 0 Solving 1 + -9x = 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 + -9x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -9x = 0 + -1 -9x = 0 + -1 Combine like terms: 0 + -1 = -1 -9x = -1 Divide each side by '-9'. x = 0.1111111111 Simplifying x = 0.1111111111

Solution

x = {0.1111111111, 0.1111111111}

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