(2x+3)(x-8)=75

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Solution for (2x+3)(x-8)=75 equation: 


Simplifying
(2x + 3)(x + -8) = 75

Reorder the terms:
(3 + 2x)(x + -8) = 75

Reorder the terms:
(3 + 2x)(-8 + x) = 75

Multiply (3 + 2x) * (-8 + x)
(3(-8 + x) + 2x * (-8 + x)) = 75
((-8 * 3 + x * 3) + 2x * (-8 + x)) = 75
((-24 + 3x) + 2x * (-8 + x)) = 75
(-24 + 3x + (-8 * 2x + x * 2x)) = 75
(-24 + 3x + (-16x + 2x2)) = 75

Combine like terms: 3x + -16x = -13x
(-24 + -13x + 2x2) = 75

Solving
-24 + -13x + 2x2 = 75

Solving for variable 'x'.

Reorder the terms:
-24 + -75 + -13x + 2x2 = 75 + -75

Combine like terms: -24 + -75 = -99
-99 + -13x + 2x2 = 75 + -75

Combine like terms: 75 + -75 = 0
-99 + -13x + 2x2 = 0

Factor a trinomial.
(-9 + -2x)(11 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5

Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-4.5, 11}

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