(2x+3)(3x-2)=63

Solution for (2x+3)(3x-2)=63 equation:

Simplifying
(2x + 3)(3x + -2) = 63

Reorder the terms:
(3 + 2x)(3x + -2) = 63

Reorder the terms:
(3 + 2x)(-2 + 3x) = 63

Multiply (3 + 2x) * (-2 + 3x)
(3(-2 + 3x) + 2x * (-2 + 3x)) = 63
((-2 * 3 + 3x * 3) + 2x * (-2 + 3x)) = 63
((-6 + 9x) + 2x * (-2 + 3x)) = 63
(-6 + 9x + (-2 * 2x + 3x * 2x)) = 63
(-6 + 9x + (-4x + 6x2)) = 63

Combine like terms: 9x + -4x = 5x
(-6 + 5x + 6x2) = 63

Solving
-6 + 5x + 6x2 = 63

Solving for variable 'x'.

Reorder the terms:
-6 + -63 + 5x + 6x2 = 63 + -63

Combine like terms: -6 + -63 = -69
-69 + 5x + 6x2 = 63 + -63

Combine like terms: 63 + -63 = 0
-69 + 5x + 6x2 = 0

Factor a trinomial.
(-23 + -6x)(3 + -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 '(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
Solution
x = {-3.833333333, 3}