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

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


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

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

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

Multiply (5 + x) * (-5 + 2x)
0 = (5(-5 + 2x) + x(-5 + 2x))
0 = ((-5 * 5 + 2x * 5) + x(-5 + 2x))
0 = ((-25 + 10x) + x(-5 + 2x))
0 = (-25 + 10x + (-5 * x + 2x * x))
0 = (-25 + 10x + (-5x + 2x2))

Combine like terms: 10x + -5x = 5x
0 = (-25 + 5x + 2x2)

Solving
0 = -25 + 5x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 25 = 25
25 + -5x + -2x2 = -25 + 5x + 2x2 + 25 + -5x + -2x2

Reorder the terms:
25 + -5x + -2x2 = -25 + 25 + 5x + -5x + 2x2 + -2x2

Combine like terms: -25 + 25 = 0
25 + -5x + -2x2 = 0 + 5x + -5x + 2x2 + -2x2
25 + -5x + -2x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
25 + -5x + -2x2 = 0 + 2x2 + -2x2
25 + -5x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
25 + -5x + -2x2 = 0

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


Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

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

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

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5

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 = {2.5, -5}

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