(x-3)(x-2)=90

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Solution for (x-3)(x-2)=90 equation: 


Simplifying
(x + -3)(x + -2) = 90

Reorder the terms:
(-3 + x)(x + -2) = 90

Reorder the terms:
(-3 + x)(-2 + x) = 90

Multiply (-3 + x) * (-2 + x)
(-3(-2 + x) + x(-2 + x)) = 90
((-2 * -3 + x * -3) + x(-2 + x)) = 90
((6 + -3x) + x(-2 + x)) = 90
(6 + -3x + (-2 * x + x * x)) = 90
(6 + -3x + (-2x + x2)) = 90

Combine like terms: -3x + -2x = -5x
(6 + -5x + x2) = 90

Solving
6 + -5x + x2 = 90

Solving for variable 'x'.

Reorder the terms:
6 + -90 + -5x + x2 = 90 + -90

Combine like terms: 6 + -90 = -84
-84 + -5x + x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-84 + -5x + x2 = 0

Factor a trinomial.
(-7 + -1x)(12 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-7, 12}

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