5x(x+2)=(x-1)(x+2)

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Solution for 5x(x+2)=(x-1)(x+2) equation: 


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

Reorder the terms:
5x(2 + x) = (x + -1)(x + 2)
(2 * 5x + x * 5x) = (x + -1)(x + 2)
(10x + 5x2) = (x + -1)(x + 2)

Reorder the terms:
10x + 5x2 = (-1 + x)(x + 2)

Reorder the terms:
10x + 5x2 = (-1 + x)(2 + x)

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

Combine like terms: -1x + 2x = 1x
10x + 5x2 = (-2 + 1x + x2)

Solving
10x + 5x2 = -2 + 1x + x2

Solving for variable 'x'.

Reorder the terms:
2 + 10x + -1x + 5x2 + -1x2 = -2 + 1x + x2 + 2 + -1x + -1x2

Combine like terms: 10x + -1x = 9x
2 + 9x + 5x2 + -1x2 = -2 + 1x + x2 + 2 + -1x + -1x2

Combine like terms: 5x2 + -1x2 = 4x2
2 + 9x + 4x2 = -2 + 1x + x2 + 2 + -1x + -1x2

Reorder the terms:
2 + 9x + 4x2 = -2 + 2 + 1x + -1x + x2 + -1x2

Combine like terms: -2 + 2 = 0
2 + 9x + 4x2 = 0 + 1x + -1x + x2 + -1x2
2 + 9x + 4x2 = 1x + -1x + x2 + -1x2

Combine like terms: 1x + -1x = 0
2 + 9x + 4x2 = 0 + x2 + -1x2
2 + 9x + 4x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + 9x + 4x2 = 0

Factor a trinomial.
(2 + x)(1 + 4x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {-2, -0.25}

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