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

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


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

Reorder the terms:
5x(2 + x) = (4x + -5)(x + 2)
(2 * 5x + x * 5x) = (4x + -5)(x + 2)
(10x + 5x2) = (4x + -5)(x + 2)

Reorder the terms:
10x + 5x2 = (-5 + 4x)(x + 2)

Reorder the terms:
10x + 5x2 = (-5 + 4x)(2 + x)

Multiply (-5 + 4x) * (2 + x)
10x + 5x2 = (-5(2 + x) + 4x * (2 + x))
10x + 5x2 = ((2 * -5 + x * -5) + 4x * (2 + x))
10x + 5x2 = ((-10 + -5x) + 4x * (2 + x))
10x + 5x2 = (-10 + -5x + (2 * 4x + x * 4x))
10x + 5x2 = (-10 + -5x + (8x + 4x2))

Combine like terms: -5x + 8x = 3x
10x + 5x2 = (-10 + 3x + 4x2)

Solving
10x + 5x2 = -10 + 3x + 4x2

Solving for variable 'x'.

Reorder the terms:
10 + 10x + -3x + 5x2 + -4x2 = -10 + 3x + 4x2 + 10 + -3x + -4x2

Combine like terms: 10x + -3x = 7x
10 + 7x + 5x2 + -4x2 = -10 + 3x + 4x2 + 10 + -3x + -4x2

Combine like terms: 5x2 + -4x2 = 1x2
10 + 7x + 1x2 = -10 + 3x + 4x2 + 10 + -3x + -4x2

Reorder the terms:
10 + 7x + 1x2 = -10 + 10 + 3x + -3x + 4x2 + -4x2

Combine like terms: -10 + 10 = 0
10 + 7x + 1x2 = 0 + 3x + -3x + 4x2 + -4x2
10 + 7x + 1x2 = 3x + -3x + 4x2 + -4x2

Combine like terms: 3x + -3x = 0
10 + 7x + 1x2 = 0 + 4x2 + -4x2
10 + 7x + 1x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
10 + 7x + 1x2 = 0

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


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

Simplifying
5 + x = 0

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

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

Combine like terms: 0 + -5 = -5
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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