X^2+3X=4X+20

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Solution for X^2+3X=4X+20 equation: 


Simplifying
X2 + 3X = 4X + 20

Reorder the terms:
3X + X2 = 4X + 20

Reorder the terms:
3X + X2 = 20 + 4X

Solving
3X + X2 = 20 + 4X

Solving for variable 'X'.

Reorder the terms:
-20 + 3X + -4X + X2 = 20 + 4X + -20 + -4X

Combine like terms: 3X + -4X = -1X
-20 + -1X + X2 = 20 + 4X + -20 + -4X

Reorder the terms:
-20 + -1X + X2 = 20 + -20 + 4X + -4X

Combine like terms: 20 + -20 = 0
-20 + -1X + X2 = 0 + 4X + -4X
-20 + -1X + X2 = 4X + -4X

Combine like terms: 4X + -4X = 0
-20 + -1X + X2 = 0

Factor a trinomial.
(-4 + -1X)(5 + -1X) = 0


Subproblem 1
Set the factor '(-4 + -1X)' equal to zero and attempt to solve:

Simplifying
-4 + -1X = 0

Solving
-4 + -1X = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1X = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1X = 0 + 4
-1X = 0 + 4

Combine like terms: 0 + 4 = 4
-1X = 4

Divide each side by '-1'.
X = -4

Simplifying
X = -4

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 = {-4, 5}

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