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

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


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

Reorder the terms:
(-2 + 3x)(2x + 1) = 5

Reorder the terms:
(-2 + 3x)(1 + 2x) = 5

Multiply (-2 + 3x) * (1 + 2x)
(-2(1 + 2x) + 3x * (1 + 2x)) = 5
((1 * -2 + 2x * -2) + 3x * (1 + 2x)) = 5
((-2 + -4x) + 3x * (1 + 2x)) = 5
(-2 + -4x + (1 * 3x + 2x * 3x)) = 5
(-2 + -4x + (3x + 6x2)) = 5

Combine like terms: -4x + 3x = -1x
(-2 + -1x + 6x2) = 5

Solving
-2 + -1x + 6x2 = 5

Solving for variable 'x'.

Reorder the terms:
-2 + -5 + -1x + 6x2 = 5 + -5

Combine like terms: -2 + -5 = -7
-7 + -1x + 6x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-7 + -1x + 6x2 = 0

Factor a trinomial.
(-1 + -1x)(7 + -6x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -6x)' equal to zero and attempt to solve:

Simplifying
7 + -6x = 0

Solving
7 + -6x = 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 + -6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x = 0 + -7
-6x = 0 + -7

Combine like terms: 0 + -7 = -7
-6x = -7

Divide each side by '-6'.
x = 1.166666667

Simplifying
x = 1.166666667
Solution
x = {-1, 1.166666667}

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