(x-4)(x-5)=90

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Solution for (x-4)(x-5)=90 equation: 


Simplifying
(x + -4)(x + -5) = 90

Reorder the terms:
(-4 + x)(x + -5) = 90

Reorder the terms:
(-4 + x)(-5 + x) = 90

Multiply (-4 + x) * (-5 + x)
(-4(-5 + x) + x(-5 + x)) = 90
((-5 * -4 + x * -4) + x(-5 + x)) = 90
((20 + -4x) + x(-5 + x)) = 90
(20 + -4x + (-5 * x + x * x)) = 90
(20 + -4x + (-5x + x2)) = 90

Combine like terms: -4x + -5x = -9x
(20 + -9x + x2) = 90

Solving
20 + -9x + x2 = 90

Solving for variable 'x'.

Reorder the terms:
20 + -90 + -9x + x2 = 90 + -90

Combine like terms: 20 + -90 = -70
-70 + -9x + x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-70 + -9x + x2 = 0

Factor a trinomial.
(-5 + -1x)(14 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
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
Solution
x = {-5, 14}

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