(x-7)(x+17)=25

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Solution for (x-7)(x+17)=25 equation: 


Simplifying
(x + -7)(x + 17) = 25

Reorder the terms:
(-7 + x)(x + 17) = 25

Reorder the terms:
(-7 + x)(17 + x) = 25

Multiply (-7 + x) * (17 + x)
(-7(17 + x) + x(17 + x)) = 25
((17 * -7 + x * -7) + x(17 + x)) = 25
((-119 + -7x) + x(17 + x)) = 25
(-119 + -7x + (17 * x + x * x)) = 25
(-119 + -7x + (17x + x2)) = 25

Combine like terms: -7x + 17x = 10x
(-119 + 10x + x2) = 25

Solving
-119 + 10x + x2 = 25

Solving for variable 'x'.

Reorder the terms:
-119 + -25 + 10x + x2 = 25 + -25

Combine like terms: -119 + -25 = -144
-144 + 10x + x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-144 + 10x + x2 = 0

Factor a trinomial.
(-18 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-18 + -1x)' equal to zero and attempt to solve:

Simplifying
-18 + -1x = 0

Solving
-18 + -1x = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1x = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1x = 0 + 18
-1x = 0 + 18

Combine like terms: 0 + 18 = 18
-1x = 18

Divide each side by '-1'.
x = -18

Simplifying
x = -18

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 = {-18, 8}

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