4X^2+10X=X^2-X+4

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Solution for 4X^2+10X=X^2-X+4 equation: 


Simplifying
4X2 + 10X = X2 + -1X + 4

Reorder the terms:
10X + 4X2 = X2 + -1X + 4

Reorder the terms:
10X + 4X2 = 4 + -1X + X2

Solving
10X + 4X2 = 4 + -1X + X2

Solving for variable 'X'.

Reorder the terms:
-4 + 10X + X + 4X2 + -1X2 = 4 + -1X + X2 + -4 + X + -1X2

Combine like terms: 10X + X = 11X
-4 + 11X + 4X2 + -1X2 = 4 + -1X + X2 + -4 + X + -1X2

Combine like terms: 4X2 + -1X2 = 3X2
-4 + 11X + 3X2 = 4 + -1X + X2 + -4 + X + -1X2

Reorder the terms:
-4 + 11X + 3X2 = 4 + -4 + -1X + X + X2 + -1X2

Combine like terms: 4 + -4 = 0
-4 + 11X + 3X2 = 0 + -1X + X + X2 + -1X2
-4 + 11X + 3X2 = -1X + X + X2 + -1X2

Combine like terms: -1X + X = 0
-4 + 11X + 3X2 = 0 + X2 + -1X2
-4 + 11X + 3X2 = X2 + -1X2

Combine like terms: X2 + -1X2 = 0
-4 + 11X + 3X2 = 0

Factor a trinomial.
(-4 + -1X)(1 + -3X) = 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 '(1 + -3X)' equal to zero and attempt to solve:

Simplifying
1 + -3X = 0

Solving
1 + -3X = 0

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

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

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

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

Divide each side by '-3'.
X = 0.3333333333

Simplifying
X = 0.3333333333
Solution
X = {-4, 0.3333333333}

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