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

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Solution for 0=(x+1)(2x-4) equation: 


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

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

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

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

Combine like terms: 2x + -4x = -2x
0 = (-4 + -2x + 2x2)

Solving
0 = -4 + -2x + 2x2

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + x + -1x2) = 0

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

Ignore the factor 2.

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {2, -1}

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