(3x+5)(2x-3)=-8

Solution for (3x+5)(2x-3)=-8 equation:

Simplifying
(3x + 5)(2x + -3) = -8

Reorder the terms:
(5 + 3x)(2x + -3) = -8

Reorder the terms:
(5 + 3x)(-3 + 2x) = -8

Multiply (5 + 3x) * (-3 + 2x)
(5(-3 + 2x) + 3x * (-3 + 2x)) = -8
((-3 * 5 + 2x * 5) + 3x * (-3 + 2x)) = -8
((-15 + 10x) + 3x * (-3 + 2x)) = -8
(-15 + 10x + (-3 * 3x + 2x * 3x)) = -8
(-15 + 10x + (-9x + 6x2)) = -8

Combine like terms: 10x + -9x = 1x
(-15 + 1x + 6x2) = -8

Solving
-15 + 1x + 6x2 = -8

Solving for variable 'x'.

Reorder the terms:
-15 + 8 + 1x + 6x2 = -8 + 8

Combine like terms: -15 + 8 = -7
-7 + 1x + 6x2 = -8 + 8

Combine like terms: -8 + 8 = 0
-7 + 1x + 6x2 = 0

Factor a trinomial.
(-7 + -6x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-7 + -6x)' equal to zero and attempt to solve:

Simplifying
-7 + -6x = 0

Solving
-7 + -6x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -6x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -6x = 0 + 7
-6x = 0 + 7

Combine like terms: 0 + 7 = 7
-6x = 7

Divide each side by '-6'.
x = -1.166666667

Simplifying
x = -1.166666667
Subproblem 2
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
Solution
x = {-1.166666667, 1}