(3x-8)(2x+3)=150

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Solution for (3x-8)(2x+3)=150 equation: 


Simplifying
(3x + -8)(2x + 3) = 150

Reorder the terms:
(-8 + 3x)(2x + 3) = 150

Reorder the terms:
(-8 + 3x)(3 + 2x) = 150

Multiply (-8 + 3x) * (3 + 2x)
(-8(3 + 2x) + 3x * (3 + 2x)) = 150
((3 * -8 + 2x * -8) + 3x * (3 + 2x)) = 150
((-24 + -16x) + 3x * (3 + 2x)) = 150
(-24 + -16x + (3 * 3x + 2x * 3x)) = 150
(-24 + -16x + (9x + 6x2)) = 150

Combine like terms: -16x + 9x = -7x
(-24 + -7x + 6x2) = 150

Solving
-24 + -7x + 6x2 = 150

Solving for variable 'x'.

Reorder the terms:
-24 + -150 + -7x + 6x2 = 150 + -150

Combine like terms: -24 + -150 = -174
-174 + -7x + 6x2 = 150 + -150

Combine like terms: 150 + -150 = 0
-174 + -7x + 6x2 = 0

Factor a trinomial.
(-29 + -6x)(6 + -1x) = 0


Subproblem 1
Set the factor '(-29 + -6x)' equal to zero and attempt to solve:

Simplifying
-29 + -6x = 0

Solving
-29 + -6x = 0

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

Add '29' to each side of the equation.
-29 + 29 + -6x = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -6x = 0 + 29
-6x = 0 + 29

Combine like terms: 0 + 29 = 29
-6x = 29

Divide each side by '-6'.
x = -4.833333333

Simplifying
x = -4.833333333

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-4.833333333, 6}

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