(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.
(-8 + -3x)(3 + -1x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-2.666666667, 3}

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