(2x+3)(3x-1)=52

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Solution for (2x+3)(3x-1)=52 equation: 


Simplifying
(2x + 3)(3x + -1) = 52

Reorder the terms:
(3 + 2x)(3x + -1) = 52

Reorder the terms:
(3 + 2x)(-1 + 3x) = 52

Multiply (3 + 2x) * (-1 + 3x)
(3(-1 + 3x) + 2x * (-1 + 3x)) = 52
((-1 * 3 + 3x * 3) + 2x * (-1 + 3x)) = 52
((-3 + 9x) + 2x * (-1 + 3x)) = 52
(-3 + 9x + (-1 * 2x + 3x * 2x)) = 52
(-3 + 9x + (-2x + 6x2)) = 52

Combine like terms: 9x + -2x = 7x
(-3 + 7x + 6x2) = 52

Solving
-3 + 7x + 6x2 = 52

Solving for variable 'x'.

Reorder the terms:
-3 + -52 + 7x + 6x2 = 52 + -52

Combine like terms: -3 + -52 = -55
-55 + 7x + 6x2 = 52 + -52

Combine like terms: 52 + -52 = 0
-55 + 7x + 6x2 = 0

Factor a trinomial.
(-11 + -3x)(5 + -2x) = 0


Subproblem 1
Set the factor '(-11 + -3x)' equal to zero and attempt to solve:

Simplifying
-11 + -3x = 0

Solving
-11 + -3x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -3x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3x = 0 + 11
-3x = 0 + 11

Combine like terms: 0 + 11 = 11
-3x = 11

Divide each side by '-3'.
x = -3.666666667

Simplifying
x = -3.666666667

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-3.666666667, 2.5}

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