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

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Solution for 0=(2x-1)(x+5) equation: 


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

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

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

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

Combine like terms: -1x + 10x = 9x
0 = (-5 + 9x + 2x2)

Solving
0 = -5 + 9x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 5 = 5
5 + -9x + -2x2 = -5 + 9x + 2x2 + 5 + -9x + -2x2

Reorder the terms:
5 + -9x + -2x2 = -5 + 5 + 9x + -9x + 2x2 + -2x2

Combine like terms: -5 + 5 = 0
5 + -9x + -2x2 = 0 + 9x + -9x + 2x2 + -2x2
5 + -9x + -2x2 = 9x + -9x + 2x2 + -2x2

Combine like terms: 9x + -9x = 0
5 + -9x + -2x2 = 0 + 2x2 + -2x2
5 + -9x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5 + -9x + -2x2 = 0

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


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

Simplifying
1 + -2x = 0

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
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
Solution
x = {0.5, -5}

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