(3x+4)(2x-1)=65

Solution for (3x+4)(2x-1)=65 equation:

Simplifying
(3x + 4)(2x + -1) = 65

Reorder the terms:
(4 + 3x)(2x + -1) = 65

Reorder the terms:
(4 + 3x)(-1 + 2x) = 65

Multiply (4 + 3x) * (-1 + 2x)
(4(-1 + 2x) + 3x * (-1 + 2x)) = 65
((-1 * 4 + 2x * 4) + 3x * (-1 + 2x)) = 65
((-4 + 8x) + 3x * (-1 + 2x)) = 65
(-4 + 8x + (-1 * 3x + 2x * 3x)) = 65
(-4 + 8x + (-3x + 6x2)) = 65

Combine like terms: 8x + -3x = 5x
(-4 + 5x + 6x2) = 65

Solving
-4 + 5x + 6x2 = 65

Solving for variable 'x'.

Reorder the terms:
-4 + -65 + 5x + 6x2 = 65 + -65

Combine like terms: -4 + -65 = -69
-69 + 5x + 6x2 = 65 + -65

Combine like terms: 65 + -65 = 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}