0=-x^2+4x+5

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Solution for 0=-x^2+4x+5 equation: 


Simplifying
0 = -1x2 + 4x + 5

Reorder the terms:
0 = 5 + 4x + -1x2

Solving
0 = 5 + 4x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + -4x + x2 = 5 + 4x + -1x2 + -5 + -4x + x2

Reorder the terms:
-5 + -4x + x2 = 5 + -5 + 4x + -4x + -1x2 + x2

Combine like terms: 5 + -5 = 0
-5 + -4x + x2 = 0 + 4x + -4x + -1x2 + x2
-5 + -4x + x2 = 4x + -4x + -1x2 + x2

Combine like terms: 4x + -4x = 0
-5 + -4x + x2 = 0 + -1x2 + x2
-5 + -4x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-5 + -4x + x2 = 0

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


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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1

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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-1, 5}

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