K(x-2)(x-7)=0

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Solution for K(x-2)(x-7)=0 equation:


Simplifying
K(x + -2)(x + -7) = 0

Reorder the terms:
K(-2 + x)(x + -7) = 0

Reorder the terms:
K(-2 + x)(-7 + x) = 0

Multiply (-2 + x) * (-7 + x)
K(-2(-7 + x) + x(-7 + x)) = 0
K((-7 * -2 + x * -2) + x(-7 + x)) = 0
K((14 + -2x) + x(-7 + x)) = 0
K(14 + -2x + (-7 * x + x * x)) = 0
K(14 + -2x + (-7x + x2)) = 0

Combine like terms: -2x + -7x = -9x
K(14 + -9x + x2) = 0
(14 * K + -9x * K + x2 * K) = 0
(14K + -9xK + x2K) = 0

Solving
14K + -9xK + x2K = 0

Solving for variable 'K'.

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

Factor out the Greatest Common Factor (GCF), 'K'.
K(14 + -9x + x2) = 0

Factor a trinomial.
K((2 + -1x)(7 + -1x)) = 0

Subproblem 1

Set the factor 'K' equal to zero and attempt to solve: Simplifying K = 0 Solving K = 0 Move all terms containing K to the left, all other terms to the right. Simplifying K = 0

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing K to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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 '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing K to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Add 'x' to each side of the equation. -1x + x = -7 + x Combine like terms: -1x + x = 0 0 = -7 + x Simplifying 0 = -7 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

K = {0}

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