6x-5=x^2-4x+20

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Solution for 6x-5=x^2-4x+20 equation:


Simplifying
6x + -5 = x2 + -4x + 20

Reorder the terms:
-5 + 6x = x2 + -4x + 20

Reorder the terms:
-5 + 6x = 20 + -4x + x2

Solving
-5 + 6x = 20 + -4x + x2

Solving for variable 'x'.

Reorder the terms:
-5 + -20 + 6x + 4x + -1x2 = 20 + -4x + x2 + -20 + 4x + -1x2

Combine like terms: -5 + -20 = -25
-25 + 6x + 4x + -1x2 = 20 + -4x + x2 + -20 + 4x + -1x2

Combine like terms: 6x + 4x = 10x
-25 + 10x + -1x2 = 20 + -4x + x2 + -20 + 4x + -1x2

Reorder the terms:
-25 + 10x + -1x2 = 20 + -20 + -4x + 4x + x2 + -1x2

Combine like terms: 20 + -20 = 0
-25 + 10x + -1x2 = 0 + -4x + 4x + x2 + -1x2
-25 + 10x + -1x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
-25 + 10x + -1x2 = 0 + x2 + -1x2
-25 + 10x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-25 + 10x + -1x2 = 0

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


Subproblem 1
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

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 = {5, 5}

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