(4x+3)(2-3x)=6

Solution for (4x+3)(2-3x)=6 equation:

Simplifying
(4x + 3)(2 + -3x) = 6

Reorder the terms:
(3 + 4x)(2 + -3x) = 6

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

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

Add '-6' to each side of the equation.
6 + -1x + -6 + -12x2 = 6 + -6

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

Combine like terms: 6 + -6 = 0
0 + -1x + -12x2 = 6 + -6
-1x + -12x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-1x + -12x2 = 0

Solving
-1x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(1 + 12x) = 0

Ignore the factor -1.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(1 + 12x)' equal to zero and attempt to solve:

Simplifying
1 + 12x = 0

Solving
1 + 12x = 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 + 12x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 12x = 0 + -1
12x = 0 + -1

Combine like terms: 0 + -1 = -1
12x = -1

Divide each side by '12'.
x = -0.08333333333

Simplifying
x = -0.08333333333
Solution
x = {0, -0.08333333333}