(2x+1)(3x-1)=14(x+1)

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Solution for (2x+1)(3x-1)=14(x+1) equation: 


Simplifying
(2x + 1)(3x + -1) = 14(x + 1)

Reorder the terms:
(1 + 2x)(3x + -1) = 14(x + 1)

Reorder the terms:
(1 + 2x)(-1 + 3x) = 14(x + 1)

Multiply (1 + 2x) * (-1 + 3x)
(1(-1 + 3x) + 2x * (-1 + 3x)) = 14(x + 1)
((-1 * 1 + 3x * 1) + 2x * (-1 + 3x)) = 14(x + 1)
((-1 + 3x) + 2x * (-1 + 3x)) = 14(x + 1)
(-1 + 3x + (-1 * 2x + 3x * 2x)) = 14(x + 1)
(-1 + 3x + (-2x + 6x2)) = 14(x + 1)

Combine like terms: 3x + -2x = 1x
(-1 + 1x + 6x2) = 14(x + 1)

Reorder the terms:
-1 + 1x + 6x2 = 14(1 + x)
-1 + 1x + 6x2 = (1 * 14 + x * 14)
-1 + 1x + 6x2 = (14 + 14x)

Solving
-1 + 1x + 6x2 = 14 + 14x

Solving for variable 'x'.

Reorder the terms:
-1 + -14 + 1x + -14x + 6x2 = 14 + 14x + -14 + -14x

Combine like terms: -1 + -14 = -15
-15 + 1x + -14x + 6x2 = 14 + 14x + -14 + -14x

Combine like terms: 1x + -14x = -13x
-15 + -13x + 6x2 = 14 + 14x + -14 + -14x

Reorder the terms:
-15 + -13x + 6x2 = 14 + -14 + 14x + -14x

Combine like terms: 14 + -14 = 0
-15 + -13x + 6x2 = 0 + 14x + -14x
-15 + -13x + 6x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-15 + -13x + 6x2 = 0

Factor a trinomial.
(-5 + -6x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -6x)' equal to zero and attempt to solve:

Simplifying
-5 + -6x = 0

Solving
-5 + -6x = 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 + -6x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6x = 0 + 5
-6x = 0 + 5

Combine like terms: 0 + 5 = 5
-6x = 5

Divide each side by '-6'.
x = -0.8333333333

Simplifying
x = -0.8333333333

Subproblem 2
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
Solution
x = {-0.8333333333, 3}

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