x^2-3x-20=40+4x

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Solution for x^2-3x-20=40+4x equation: 


Simplifying
x2 + -3x + -20 = 40 + 4x

Reorder the terms:
-20 + -3x + x2 = 40 + 4x

Solving
-20 + -3x + x2 = 40 + 4x

Solving for variable 'x'.

Reorder the terms:
-20 + -40 + -3x + -4x + x2 = 40 + 4x + -40 + -4x

Combine like terms: -20 + -40 = -60
-60 + -3x + -4x + x2 = 40 + 4x + -40 + -4x

Combine like terms: -3x + -4x = -7x
-60 + -7x + x2 = 40 + 4x + -40 + -4x

Reorder the terms:
-60 + -7x + x2 = 40 + -40 + 4x + -4x

Combine like terms: 40 + -40 = 0
-60 + -7x + x2 = 0 + 4x + -4x
-60 + -7x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-60 + -7x + x2 = 0

Factor a trinomial.
(-5 + -1x)(12 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-5, 12}

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