(2x+3)(3x-4)=-7

Solution for (2x+3)(3x-4)=-7 equation:

Simplifying
(2x + 3)(3x + -4) = -7

Reorder the terms:
(3 + 2x)(3x + -4) = -7

Reorder the terms:
(3 + 2x)(-4 + 3x) = -7

Multiply (3 + 2x) * (-4 + 3x)
(3(-4 + 3x) + 2x * (-4 + 3x)) = -7
((-4 * 3 + 3x * 3) + 2x * (-4 + 3x)) = -7
((-12 + 9x) + 2x * (-4 + 3x)) = -7
(-12 + 9x + (-4 * 2x + 3x * 2x)) = -7
(-12 + 9x + (-8x + 6x2)) = -7

Combine like terms: 9x + -8x = 1x
(-12 + 1x + 6x2) = -7

Solving
-12 + 1x + 6x2 = -7

Solving for variable 'x'.

Reorder the terms:
-12 + 7 + 1x + 6x2 = -7 + 7

Combine like terms: -12 + 7 = -5
-5 + 1x + 6x2 = -7 + 7

Combine like terms: -7 + 7 = 0
-5 + 1x + 6x2 = 0

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

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

Simplifying
-1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = -1

Simplifying
x = -1
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 = {-1, 0.8333333333}