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

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


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

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

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

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

Combine like terms: 2x + -5x = -3x
0 = (-5 + -3x + 2x2)

Solving
0 = -5 + -3x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 5 = 5
5 + 3x + -2x2 = -5 + -3x + 2x2 + 5 + 3x + -2x2

Reorder the terms:
5 + 3x + -2x2 = -5 + 5 + -3x + 3x + 2x2 + -2x2

Combine like terms: -5 + 5 = 0
5 + 3x + -2x2 = 0 + -3x + 3x + 2x2 + -2x2
5 + 3x + -2x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
5 + 3x + -2x2 = 0 + 2x2 + -2x2
5 + 3x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5 + 3x + -2x2 = 0

Factor a trinomial.
(5 + -2x)(1 + 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 '(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 = {2.5, -1}

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