26x^3y^4z^2+14x^2y^6=2x^2y^4z^2(13x+7y^2z^2)

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Solution for 26x^3y^4z^2+14x^2y^6=2x^2y^4z^2(13x+7y^2z^2) equation:


Simplifying
26x3y4z2 + 14x2y6 = 2x2y4z2(13x + 7y2z2)

Reorder the terms:
14x2y6 + 26x3y4z2 = 2x2y4z2(13x + 7y2z2)
14x2y6 + 26x3y4z2 = (13x * 2x2y4z2 + 7y2z2 * 2x2y4z2)

Reorder the terms:
14x2y6 + 26x3y4z2 = (14x2y6z4 + 26x3y4z2)
14x2y6 + 26x3y4z2 = (14x2y6z4 + 26x3y4z2)

Add '-26x3y4z2' to each side of the equation.
14x2y6 + 26x3y4z2 + -26x3y4z2 = 14x2y6z4 + 26x3y4z2 + -26x3y4z2

Combine like terms: 26x3y4z2 + -26x3y4z2 = 0
14x2y6 + 0 = 14x2y6z4 + 26x3y4z2 + -26x3y4z2
14x2y6 = 14x2y6z4 + 26x3y4z2 + -26x3y4z2

Combine like terms: 26x3y4z2 + -26x3y4z2 = 0
14x2y6 = 14x2y6z4 + 0
14x2y6 = 14x2y6z4

Solving
14x2y6 = 14x2y6z4

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-14x2y6z4' to each side of the equation.
14x2y6 + -14x2y6z4 = 14x2y6z4 + -14x2y6z4

Combine like terms: 14x2y6z4 + -14x2y6z4 = 0
14x2y6 + -14x2y6z4 = 0

Factor out the Greatest Common Factor (GCF), '14x2y6'.
14x2y6(1 + -1z4) = 0

Factor a difference between two squares.
14x2y6((1 + z2)(1 + -1z2)) = 0

Factor a difference between two squares.
14x2y6((1 + z2)((1 + z)(1 + -1z))) = 0

Ignore the factor 14.

Subproblem 1

Set the factor 'x2y6' equal to zero and attempt to solve: Simplifying x2y6 = 0 Solving x2y6 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2y6 = 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 + z2)' equal to zero and attempt to solve: Simplifying 1 + z2 = 0 Solving 1 + z2 = 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 + z2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z2 = 0 + -1 z2 = 0 + -1 Combine like terms: 0 + -1 = -1 z2 = -1 Add '-1z2' to each side of the equation. z2 + -1z2 = -1 + -1z2 Combine like terms: z2 + -1z2 = 0 0 = -1 + -1z2 Simplifying 0 = -1 + -1z2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

Set the factor '(1 + z)' equal to zero and attempt to solve: Simplifying 1 + z = 0 Solving 1 + z = 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 + z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + z = 0 + -1 z = 0 + -1 Combine like terms: 0 + -1 = -1 z = -1 Add '-1z' to each side of the equation. z + -1z = -1 + -1z Combine like terms: z + -1z = 0 0 = -1 + -1z Simplifying 0 = -1 + -1z The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 4

Set the factor '(1 + -1z)' equal to zero and attempt to solve: Simplifying 1 + -1z = 0 Solving 1 + -1z = 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 + -1z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1z = 0 + -1 -1z = 0 + -1 Combine like terms: 0 + -1 = -1 -1z = -1 Add 'z' to each side of the equation. -1z + z = -1 + z Combine like terms: -1z + z = 0 0 = -1 + z Simplifying 0 = -1 + z 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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