3X^2-X-40=X^2+2X-5

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Solution for 3X^2-X-40=X^2+2X-5 equation: 


Simplifying
3X2 + -1X + -40 = X2 + 2X + -5

Reorder the terms:
-40 + -1X + 3X2 = X2 + 2X + -5

Reorder the terms:
-40 + -1X + 3X2 = -5 + 2X + X2

Solving
-40 + -1X + 3X2 = -5 + 2X + X2

Solving for variable 'X'.

Reorder the terms:
-40 + 5 + -1X + -2X + 3X2 + -1X2 = -5 + 2X + X2 + 5 + -2X + -1X2

Combine like terms: -40 + 5 = -35
-35 + -1X + -2X + 3X2 + -1X2 = -5 + 2X + X2 + 5 + -2X + -1X2

Combine like terms: -1X + -2X = -3X
-35 + -3X + 3X2 + -1X2 = -5 + 2X + X2 + 5 + -2X + -1X2

Combine like terms: 3X2 + -1X2 = 2X2
-35 + -3X + 2X2 = -5 + 2X + X2 + 5 + -2X + -1X2

Reorder the terms:
-35 + -3X + 2X2 = -5 + 5 + 2X + -2X + X2 + -1X2

Combine like terms: -5 + 5 = 0
-35 + -3X + 2X2 = 0 + 2X + -2X + X2 + -1X2
-35 + -3X + 2X2 = 2X + -2X + X2 + -1X2

Combine like terms: 2X + -2X = 0
-35 + -3X + 2X2 = 0 + X2 + -1X2
-35 + -3X + 2X2 = X2 + -1X2

Combine like terms: X2 + -1X2 = 0
-35 + -3X + 2X2 = 0

Factor a trinomial.
(-7 + -2X)(5 + -1X) = 0


Subproblem 1
Set the factor '(-7 + -2X)' equal to zero and attempt to solve:

Simplifying
-7 + -2X = 0

Solving
-7 + -2X = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2X = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2X = 0 + 7
-2X = 0 + 7

Combine like terms: 0 + 7 = 7
-2X = 7

Divide each side by '-2'.
X = -3.5

Simplifying
X = -3.5

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 = {-3.5, 5}

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