(2x+1)(3x-2)=55

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Solution for (2x+1)(3x-2)=55 equation: 


Simplifying
(2x + 1)(3x + -2) = 55

Reorder the terms:
(1 + 2x)(3x + -2) = 55

Reorder the terms:
(1 + 2x)(-2 + 3x) = 55

Multiply (1 + 2x) * (-2 + 3x)
(1(-2 + 3x) + 2x * (-2 + 3x)) = 55
((-2 * 1 + 3x * 1) + 2x * (-2 + 3x)) = 55
((-2 + 3x) + 2x * (-2 + 3x)) = 55
(-2 + 3x + (-2 * 2x + 3x * 2x)) = 55
(-2 + 3x + (-4x + 6x2)) = 55

Combine like terms: 3x + -4x = -1x
(-2 + -1x + 6x2) = 55

Solving
-2 + -1x + 6x2 = 55

Solving for variable 'x'.

Reorder the terms:
-2 + -55 + -1x + 6x2 = 55 + -55

Combine like terms: -2 + -55 = -57
-57 + -1x + 6x2 = 55 + -55

Combine like terms: 55 + -55 = 0
-57 + -1x + 6x2 = 0

Factor a trinomial.
(-3 + -1x)(19 + -6x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(19 + -6x)' equal to zero and attempt to solve:

Simplifying
19 + -6x = 0

Solving
19 + -6x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -6x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -6x = 0 + -19
-6x = 0 + -19

Combine like terms: 0 + -19 = -19
-6x = -19

Divide each side by '-6'.
x = 3.166666667

Simplifying
x = 3.166666667
Solution
x = {-3, 3.166666667}

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