(x-7)(x+2)=x*x+kx-14

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Solution for (x-7)(x+2)=x*x+kx-14 equation:


Simplifying
(x + -7)(x + 2) = x * x + kx + -14

Reorder the terms:
(-7 + x)(x + 2) = x * x + kx + -14

Reorder the terms:
(-7 + x)(2 + x) = x * x + kx + -14

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

Combine like terms: -7x + 2x = -5x
(-14 + -5x + x2) = x * x + kx + -14

Multiply x * x
-14 + -5x + x2 = x2 + kx + -14

Reorder the terms:
-14 + -5x + x2 = -14 + kx + x2

Add '14' to each side of the equation.
-14 + -5x + 14 + x2 = -14 + kx + 14 + x2

Reorder the terms:
-14 + 14 + -5x + x2 = -14 + kx + 14 + x2

Combine like terms: -14 + 14 = 0
0 + -5x + x2 = -14 + kx + 14 + x2
-5x + x2 = -14 + kx + 14 + x2

Reorder the terms:
-5x + x2 = -14 + 14 + kx + x2

Combine like terms: -14 + 14 = 0
-5x + x2 = 0 + kx + x2
-5x + x2 = kx + x2

Add '-1x2' to each side of the equation.
-5x + x2 + -1x2 = kx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5x + 0 = kx + x2 + -1x2
-5x = kx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5x = kx + 0
-5x = kx

Solving
-5x = kx

Solving for variable 'x'.

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

Add '-1kx' to each side of the equation.
-1kx + -5x = kx + -1kx

Combine like terms: kx + -1kx = 0
-1kx + -5x = 0

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(k + 5) = 0

Ignore the factor -1.

Subproblem 1

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

Subproblem 2

Set the factor '(k + 5)' equal to zero and attempt to solve: Simplifying k + 5 = 0 Reorder the terms: 5 + k = 0 Solving 5 + k = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + k = 0 + -5 k = 0 + -5 Combine like terms: 0 + -5 = -5 k = -5 Add '-1k' to each side of the equation. k + -1k = -5 + -1k Combine like terms: k + -1k = 0 0 = -5 + -1k Simplifying 0 = -5 + -1k The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

x = {0}

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