(3x+5)(x-6)=8

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Solution for (3x+5)(x-6)=8 equation: 


Simplifying
(3x + 5)(x + -6) = 8

Reorder the terms:
(5 + 3x)(x + -6) = 8

Reorder the terms:
(5 + 3x)(-6 + x) = 8

Multiply (5 + 3x) * (-6 + x)
(5(-6 + x) + 3x * (-6 + x)) = 8
((-6 * 5 + x * 5) + 3x * (-6 + x)) = 8
((-30 + 5x) + 3x * (-6 + x)) = 8
(-30 + 5x + (-6 * 3x + x * 3x)) = 8
(-30 + 5x + (-18x + 3x2)) = 8

Combine like terms: 5x + -18x = -13x
(-30 + -13x + 3x2) = 8

Solving
-30 + -13x + 3x2 = 8

Solving for variable 'x'.

Reorder the terms:
-30 + -8 + -13x + 3x2 = 8 + -8

Combine like terms: -30 + -8 = -38
-38 + -13x + 3x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-38 + -13x + 3x2 = 0

Factor a trinomial.
(-2 + -1x)(19 + -3x) = 0


Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(19 + -3x)' equal to zero and attempt to solve:

Simplifying
19 + -3x = 0

Solving
19 + -3x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -3x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -3x = 0 + -19
-3x = 0 + -19

Combine like terms: 0 + -19 = -19
-3x = -19

Divide each side by '-3'.
x = 6.333333333

Simplifying
x = 6.333333333
Solution
x = {-2, 6.333333333}

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