(x-6)(x+9)=100

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Solution for (x-6)(x+9)=100 equation: 


Simplifying
(x + -6)(x + 9) = 100

Reorder the terms:
(-6 + x)(x + 9) = 100

Reorder the terms:
(-6 + x)(9 + x) = 100

Multiply (-6 + x) * (9 + x)
(-6(9 + x) + x(9 + x)) = 100
((9 * -6 + x * -6) + x(9 + x)) = 100
((-54 + -6x) + x(9 + x)) = 100
(-54 + -6x + (9 * x + x * x)) = 100
(-54 + -6x + (9x + x2)) = 100

Combine like terms: -6x + 9x = 3x
(-54 + 3x + x2) = 100

Solving
-54 + 3x + x2 = 100

Solving for variable 'x'.

Reorder the terms:
-54 + -100 + 3x + x2 = 100 + -100

Combine like terms: -54 + -100 = -154
-154 + 3x + x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-154 + 3x + x2 = 0

Factor a trinomial.
(-14 + -1x)(11 + -1x) = 0


Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve:

Simplifying
-14 + -1x = 0

Solving
-14 + -1x = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1x = 0 + 14
-1x = 0 + 14

Combine like terms: 0 + 14 = 14
-1x = 14

Divide each side by '-1'.
x = -14

Simplifying
x = -14

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 = {-14, 11}

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