18-(x-5)(x-4)=-2

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Solution for 18-(x-5)(x-4)=-2 equation: 


Simplifying
18 + -1(x + -5)(x + -4) = -2

Reorder the terms:
18 + -1(-5 + x)(x + -4) = -2

Reorder the terms:
18 + -1(-5 + x)(-4 + x) = -2

Multiply (-5 + x) * (-4 + x)
18 + -1(-5(-4 + x) + x(-4 + x)) = -2
18 + -1((-4 * -5 + x * -5) + x(-4 + x)) = -2
18 + -1((20 + -5x) + x(-4 + x)) = -2
18 + -1(20 + -5x + (-4 * x + x * x)) = -2
18 + -1(20 + -5x + (-4x + x2)) = -2

Combine like terms: -5x + -4x = -9x
18 + -1(20 + -9x + x2) = -2
18 + (20 * -1 + -9x * -1 + x2 * -1) = -2
18 + (-20 + 9x + -1x2) = -2

Combine like terms: 18 + -20 = -2
-2 + 9x + -1x2 = -2

Add '2' to each side of the equation.
-2 + 9x + 2 + -1x2 = -2 + 2

Reorder the terms:
-2 + 2 + 9x + -1x2 = -2 + 2

Combine like terms: -2 + 2 = 0
0 + 9x + -1x2 = -2 + 2
9x + -1x2 = -2 + 2

Combine like terms: -2 + 2 = 0
9x + -1x2 = 0

Solving
9x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(9 + -1x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 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 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {0, 9}

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