X^2+3X-14=5X+1

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Solution for X^2+3X-14=5X+1 equation: 


Simplifying
X2 + 3X + -14 = 5X + 1

Reorder the terms:
-14 + 3X + X2 = 5X + 1

Reorder the terms:
-14 + 3X + X2 = 1 + 5X

Solving
-14 + 3X + X2 = 1 + 5X

Solving for variable 'X'.

Reorder the terms:
-14 + -1 + 3X + -5X + X2 = 1 + 5X + -1 + -5X

Combine like terms: -14 + -1 = -15
-15 + 3X + -5X + X2 = 1 + 5X + -1 + -5X

Combine like terms: 3X + -5X = -2X
-15 + -2X + X2 = 1 + 5X + -1 + -5X

Reorder the terms:
-15 + -2X + X2 = 1 + -1 + 5X + -5X

Combine like terms: 1 + -1 = 0
-15 + -2X + X2 = 0 + 5X + -5X
-15 + -2X + X2 = 5X + -5X

Combine like terms: 5X + -5X = 0
-15 + -2X + X2 = 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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