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

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


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

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

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

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

Combine like terms: -5x + 6x = 1x
(-10 + 1x + 3x2) = 14

Solving
-10 + 1x + 3x2 = 14

Solving for variable 'x'.

Reorder the terms:
-10 + -14 + 1x + 3x2 = 14 + -14

Combine like terms: -10 + -14 = -24
-24 + 1x + 3x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-24 + 1x + 3x2 = 0

Factor a trinomial.
(-3 + -1x)(8 + -3x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {-3, 2.666666667}

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