=(x-6)(x+9)

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


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

Reorder the terms:
0 = (-6 + x)(x + 9)

Reorder the terms:
0 = (-6 + x)(9 + x)

Multiply (-6 + x) * (9 + x)
0 = (-6(9 + x) + x(9 + x))
0 = ((9 * -6 + x * -6) + x(9 + x))
0 = ((-54 + -6x) + x(9 + x))
0 = (-54 + -6x + (9 * x + x * x))
0 = (-54 + -6x + (9x + x2))

Combine like terms: -6x + 9x = 3x
0 = (-54 + 3x + x2)

Solving
0 = -54 + 3x + x2

Solving for variable 'x'.

Combine like terms: 0 + 54 = 54
54 + -3x + -1x2 = -54 + 3x + x2 + 54 + -3x + -1x2

Reorder the terms:
54 + -3x + -1x2 = -54 + 54 + 3x + -3x + x2 + -1x2

Combine like terms: -54 + 54 = 0
54 + -3x + -1x2 = 0 + 3x + -3x + x2 + -1x2
54 + -3x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
54 + -3x + -1x2 = 0 + x2 + -1x2
54 + -3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
54 + -3x + -1x2 = 0

Factor a trinomial.
(6 + -1x)(9 + x) = 0


Subproblem 1
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

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

Simplifying
9 + x = 0

Solving
9 + x = 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 + x = 0 + -9

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

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

Simplifying
x = -9
Solution
x = {6, -9}

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