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

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


Simplifying
2x2 + -6x + -20 = x2 + -4x + -5

Reorder the terms:
-20 + -6x + 2x2 = x2 + -4x + -5

Reorder the terms:
-20 + -6x + 2x2 = -5 + -4x + x2

Solving
-20 + -6x + 2x2 = -5 + -4x + x2

Solving for variable 'x'.

Reorder the terms:
-20 + 5 + -6x + 4x + 2x2 + -1x2 = -5 + -4x + x2 + 5 + 4x + -1x2

Combine like terms: -20 + 5 = -15
-15 + -6x + 4x + 2x2 + -1x2 = -5 + -4x + x2 + 5 + 4x + -1x2

Combine like terms: -6x + 4x = -2x
-15 + -2x + 2x2 + -1x2 = -5 + -4x + x2 + 5 + 4x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-15 + -2x + 1x2 = -5 + -4x + x2 + 5 + 4x + -1x2

Reorder the terms:
-15 + -2x + 1x2 = -5 + 5 + -4x + 4x + x2 + -1x2

Combine like terms: -5 + 5 = 0
-15 + -2x + 1x2 = 0 + -4x + 4x + x2 + -1x2
-15 + -2x + 1x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
-15 + -2x + 1x2 = 0 + x2 + -1x2
-15 + -2x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-15 + -2x + 1x2 = 0

Factor a trinomial.
(-3 + -1x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

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 = {-3, 5}

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