(2+3x)(3-4x)=1+5x

Solution for (2+3x)(3-4x)=1+5x equation:

Simplifying
(2 + 3x)(3 + -4x) = 1 + 5x

Multiply (2 + 3x) * (3 + -4x)
(2(3 + -4x) + 3x * (3 + -4x)) = 1 + 5x
((3 * 2 + -4x * 2) + 3x * (3 + -4x)) = 1 + 5x
((6 + -8x) + 3x * (3 + -4x)) = 1 + 5x
(6 + -8x + (3 * 3x + -4x * 3x)) = 1 + 5x
(6 + -8x + (9x + -12x2)) = 1 + 5x

Combine like terms: -8x + 9x = 1x
(6 + 1x + -12x2) = 1 + 5x

Solving
6 + 1x + -12x2 = 1 + 5x

Solving for variable 'x'.

Reorder the terms:
6 + -1 + 1x + -5x + -12x2 = 1 + 5x + -1 + -5x

Combine like terms: 6 + -1 = 5
5 + 1x + -5x + -12x2 = 1 + 5x + -1 + -5x

Combine like terms: 1x + -5x = -4x
5 + -4x + -12x2 = 1 + 5x + -1 + -5x

Reorder the terms:
5 + -4x + -12x2 = 1 + -1 + 5x + -5x

Combine like terms: 1 + -1 = 0
5 + -4x + -12x2 = 0 + 5x + -5x
5 + -4x + -12x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
5 + -4x + -12x2 = 0

Factor a trinomial.
(1 + -2x)(5 + 6x) = 0

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
Set the factor '(5 + 6x)' equal to zero and attempt to solve:

Simplifying
5 + 6x = 0

Solving
5 + 6x = 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 + 6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6x = 0 + -5
6x = 0 + -5

Combine like terms: 0 + -5 = -5
6x = -5

Divide each side by '6'.
x = -0.8333333333

Simplifying
x = -0.8333333333
Solution
x = {0.5, -0.8333333333}