(3x+1)(2x-1)=4

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Solution for (3x+1)(2x-1)=4 equation: 


Simplifying
(3x + 1)(2x + -1) = 4

Reorder the terms:
(1 + 3x)(2x + -1) = 4

Reorder the terms:
(1 + 3x)(-1 + 2x) = 4

Multiply (1 + 3x) * (-1 + 2x)
(1(-1 + 2x) + 3x * (-1 + 2x)) = 4
((-1 * 1 + 2x * 1) + 3x * (-1 + 2x)) = 4
((-1 + 2x) + 3x * (-1 + 2x)) = 4
(-1 + 2x + (-1 * 3x + 2x * 3x)) = 4
(-1 + 2x + (-3x + 6x2)) = 4

Combine like terms: 2x + -3x = -1x
(-1 + -1x + 6x2) = 4

Solving
-1 + -1x + 6x2 = 4

Solving for variable 'x'.

Reorder the terms:
-1 + -4 + -1x + 6x2 = 4 + -4

Combine like terms: -1 + -4 = -5
-5 + -1x + 6x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-5 + -1x + 6x2 = 0

Factor a trinomial.
(-5 + -6x)(1 + -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 '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-0.8333333333, 1}

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