(3x-2)(2x+5)=36

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Solution for (3x-2)(2x+5)=36 equation: 


Simplifying
(3x + -2)(2x + 5) = 36

Reorder the terms:
(-2 + 3x)(2x + 5) = 36

Reorder the terms:
(-2 + 3x)(5 + 2x) = 36

Multiply (-2 + 3x) * (5 + 2x)
(-2(5 + 2x) + 3x * (5 + 2x)) = 36
((5 * -2 + 2x * -2) + 3x * (5 + 2x)) = 36
((-10 + -4x) + 3x * (5 + 2x)) = 36
(-10 + -4x + (5 * 3x + 2x * 3x)) = 36
(-10 + -4x + (15x + 6x2)) = 36

Combine like terms: -4x + 15x = 11x
(-10 + 11x + 6x2) = 36

Solving
-10 + 11x + 6x2 = 36

Solving for variable 'x'.

Reorder the terms:
-10 + -36 + 11x + 6x2 = 36 + -36

Combine like terms: -10 + -36 = -46
-46 + 11x + 6x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-46 + 11x + 6x2 = 0

Factor a trinomial.
(-23 + -6x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-23 + -6x)' equal to zero and attempt to solve:

Simplifying
-23 + -6x = 0

Solving
-23 + -6x = 0

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

Add '23' to each side of the equation.
-23 + 23 + -6x = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -6x = 0 + 23
-6x = 0 + 23

Combine like terms: 0 + 23 = 23
-6x = 23

Divide each side by '-6'.
x = -3.833333333

Simplifying
x = -3.833333333

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-3.833333333, 2}

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