2(x-5)-(x+4)(x-5)=0

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Solution for 2(x-5)-(x+4)(x-5)=0 equation: 


Simplifying
2(x + -5) + -1(x + 4)(x + -5) = 0

Reorder the terms:
2(-5 + x) + -1(x + 4)(x + -5) = 0
(-5 * 2 + x * 2) + -1(x + 4)(x + -5) = 0
(-10 + 2x) + -1(x + 4)(x + -5) = 0

Reorder the terms:
-10 + 2x + -1(4 + x)(x + -5) = 0

Reorder the terms:
-10 + 2x + -1(4 + x)(-5 + x) = 0

Multiply (4 + x) * (-5 + x)
-10 + 2x + -1(4(-5 + x) + x(-5 + x)) = 0
-10 + 2x + -1((-5 * 4 + x * 4) + x(-5 + x)) = 0
-10 + 2x + -1((-20 + 4x) + x(-5 + x)) = 0
-10 + 2x + -1(-20 + 4x + (-5 * x + x * x)) = 0
-10 + 2x + -1(-20 + 4x + (-5x + x2)) = 0

Combine like terms: 4x + -5x = -1x
-10 + 2x + -1(-20 + -1x + x2) = 0
-10 + 2x + (-20 * -1 + -1x * -1 + x2 * -1) = 0
-10 + 2x + (20 + 1x + -1x2) = 0

Reorder the terms:
-10 + 20 + 2x + 1x + -1x2 = 0

Combine like terms: -10 + 20 = 10
10 + 2x + 1x + -1x2 = 0

Combine like terms: 2x + 1x = 3x
10 + 3x + -1x2 = 0

Solving
10 + 3x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -1x)(2 + x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {5, -2}

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