(x+5)(x-2)=x^2+kx-10

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Solution for (x+5)(x-2)=x^2+kx-10 equation: 


Simplifying
(x + 5)(x + -2) = x2 + kx + -10

Reorder the terms:
(5 + x)(x + -2) = x2 + kx + -10

Reorder the terms:
(5 + x)(-2 + x) = x2 + kx + -10

Multiply (5 + x) * (-2 + x)
(5(-2 + x) + x(-2 + x)) = x2 + kx + -10
((-2 * 5 + x * 5) + x(-2 + x)) = x2 + kx + -10
((-10 + 5x) + x(-2 + x)) = x2 + kx + -10
(-10 + 5x + (-2 * x + x * x)) = x2 + kx + -10
(-10 + 5x + (-2x + x2)) = x2 + kx + -10

Combine like terms: 5x + -2x = 3x
(-10 + 3x + x2) = x2 + kx + -10

Reorder the terms:
-10 + 3x + x2 = -10 + kx + x2

Add '10' to each side of the equation.
-10 + 3x + 10 + x2 = -10 + kx + 10 + x2

Reorder the terms:
-10 + 10 + 3x + x2 = -10 + kx + 10 + x2

Combine like terms: -10 + 10 = 0
0 + 3x + x2 = -10 + kx + 10 + x2
3x + x2 = -10 + kx + 10 + x2

Reorder the terms:
3x + x2 = -10 + 10 + kx + x2

Combine like terms: -10 + 10 = 0
3x + x2 = 0 + kx + x2
3x + x2 = kx + x2

Add '-1x2' to each side of the equation.
3x + x2 + -1x2 = kx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3x + 0 = kx + x2 + -1x2
3x = kx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3x = kx + 0
3x = kx

Solving
3x = 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 + 3x = kx + -1kx

Combine like terms: kx + -1kx = 0
-1kx + 3x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1k + 3) = 0


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 '(-1k + 3)' equal to zero and attempt to solve:

Simplifying
-1k + 3 = 0

Reorder the terms:
3 + -1k = 0

Solving
3 + -1k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1k = 0 + -3
-1k = 0 + -3

Combine like terms: 0 + -3 = -3
-1k = -3

Add 'k' to each side of the equation.
-1k + k = -3 + k

Combine like terms: -1k + k = 0
0 = -3 + k

Simplifying
0 = -3 + k

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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