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

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

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

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

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

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

Combine like terms: 9x + -2x = 7x
(-3 + 7x + 6x2) = -4

Solving
-3 + 7x + 6x2 = -4

Solving for variable 'x'.

Reorder the terms:
-3 + 4 + 7x + 6x2 = -4 + 4

Combine like terms: -3 + 4 = 1
1 + 7x + 6x2 = -4 + 4

Combine like terms: -4 + 4 = 0
1 + 7x + 6x2 = 0

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

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(1 + 6x)' equal to zero and attempt to solve:

Simplifying
1 + 6x = 0

Solving
1 + 6x = 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 + 6x = 0 + -1

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

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

Divide each side by '6'.
x = -0.1666666667

Simplifying
x = -0.1666666667
Solution
x = {-1, -0.1666666667}