2X(3X+2)-1=5X+1

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Solution for 2X(3X+2)-1=5X+1 equation: 


Simplifying
2X(3X + 2) + -1 = 5X + 1

Reorder the terms:
2X(2 + 3X) + -1 = 5X + 1
(2 * 2X + 3X * 2X) + -1 = 5X + 1
(4X + 6X2) + -1 = 5X + 1

Reorder the terms:
-1 + 4X + 6X2 = 5X + 1

Reorder the terms:
-1 + 4X + 6X2 = 1 + 5X

Solving
-1 + 4X + 6X2 = 1 + 5X

Solving for variable 'X'.

Reorder the terms:
-1 + -1 + 4X + -5X + 6X2 = 1 + 5X + -1 + -5X

Combine like terms: -1 + -1 = -2
-2 + 4X + -5X + 6X2 = 1 + 5X + -1 + -5X

Combine like terms: 4X + -5X = -1X
-2 + -1X + 6X2 = 1 + 5X + -1 + -5X

Reorder the terms:
-2 + -1X + 6X2 = 1 + -1 + 5X + -5X

Combine like terms: 1 + -1 = 0
-2 + -1X + 6X2 = 0 + 5X + -5X
-2 + -1X + 6X2 = 5X + -5X

Combine like terms: 5X + -5X = 0
-2 + -1X + 6X2 = 0

Factor a trinomial.
(-1 + -2X)(2 + -3X) = 0


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

Simplifying
-1 + -2X = 0

Solving
-1 + -2X = 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 + -2X = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2X = 0 + 1
-2X = 0 + 1

Combine like terms: 0 + 1 = 1
-2X = 1

Divide each side by '-2'.
X = -0.5

Simplifying
X = -0.5

Subproblem 2
Set the factor '(2 + -3X)' equal to zero and attempt to solve:

Simplifying
2 + -3X = 0

Solving
2 + -3X = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3X = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3X = 0 + -2
-3X = 0 + -2

Combine like terms: 0 + -2 = -2
-3X = -2

Divide each side by '-3'.
X = 0.6666666667

Simplifying
X = 0.6666666667
Solution
X = {-0.5, 0.6666666667}

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