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

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


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

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

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

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

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

Solving
2x = -20 + 1x + x2

Solving for variable 'x'.

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

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

Reorder the terms:
20 + 1x + -1x2 = -20 + 20 + 1x + -1x + x2 + -1x2

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

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

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

Factor a trinomial.
(5 + -1x)(4 + 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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {5, -4}

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