(2x-3)(3x+5)=-14

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Solution for (2x-3)(3x+5)=-14 equation: 


Simplifying
(2x + -3)(3x + 5) = -14

Reorder the terms:
(-3 + 2x)(3x + 5) = -14

Reorder the terms:
(-3 + 2x)(5 + 3x) = -14

Multiply (-3 + 2x) * (5 + 3x)
(-3(5 + 3x) + 2x * (5 + 3x)) = -14
((5 * -3 + 3x * -3) + 2x * (5 + 3x)) = -14
((-15 + -9x) + 2x * (5 + 3x)) = -14
(-15 + -9x + (5 * 2x + 3x * 2x)) = -14
(-15 + -9x + (10x + 6x2)) = -14

Combine like terms: -9x + 10x = 1x
(-15 + 1x + 6x2) = -14

Solving
-15 + 1x + 6x2 = -14

Solving for variable 'x'.

Reorder the terms:
-15 + 14 + 1x + 6x2 = -14 + 14

Combine like terms: -15 + 14 = -1
-1 + 1x + 6x2 = -14 + 14

Combine like terms: -14 + 14 = 0
-1 + 1x + 6x2 = 0

Factor a trinomial.
(-1 + -2x)(1 + -3x) = 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 '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-0.5, 0.3333333333}

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