(2x-5)(x+7)=165

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Solution for (2x-5)(x+7)=165 equation: 


Simplifying
(2x + -5)(x + 7) = 165

Reorder the terms:
(-5 + 2x)(x + 7) = 165

Reorder the terms:
(-5 + 2x)(7 + x) = 165

Multiply (-5 + 2x) * (7 + x)
(-5(7 + x) + 2x * (7 + x)) = 165
((7 * -5 + x * -5) + 2x * (7 + x)) = 165
((-35 + -5x) + 2x * (7 + x)) = 165
(-35 + -5x + (7 * 2x + x * 2x)) = 165
(-35 + -5x + (14x + 2x2)) = 165

Combine like terms: -5x + 14x = 9x
(-35 + 9x + 2x2) = 165

Solving
-35 + 9x + 2x2 = 165

Solving for variable 'x'.

Reorder the terms:
-35 + -165 + 9x + 2x2 = 165 + -165

Combine like terms: -35 + -165 = -200
-200 + 9x + 2x2 = 165 + -165

Combine like terms: 165 + -165 = 0
-200 + 9x + 2x2 = 0

Factor a trinomial.
(-25 + -2x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-25 + -2x)' equal to zero and attempt to solve:

Simplifying
-25 + -2x = 0

Solving
-25 + -2x = 0

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

Add '25' to each side of the equation.
-25 + 25 + -2x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -2x = 0 + 25
-2x = 0 + 25

Combine like terms: 0 + 25 = 25
-2x = 25

Divide each side by '-2'.
x = -12.5

Simplifying
x = -12.5

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-12.5, 8}

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