(X-6)(X+4)=11

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Solution for (X-6)(X+4)=11 equation: 


Simplifying
(X + -6)(X + 4) = 11

Reorder the terms:
(-6 + X)(X + 4) = 11

Reorder the terms:
(-6 + X)(4 + X) = 11

Multiply (-6 + X) * (4 + X)
(-6(4 + X) + X(4 + X)) = 11
((4 * -6 + X * -6) + X(4 + X)) = 11
((-24 + -6X) + X(4 + X)) = 11
(-24 + -6X + (4 * X + X * X)) = 11
(-24 + -6X + (4X + X2)) = 11

Combine like terms: -6X + 4X = -2X
(-24 + -2X + X2) = 11

Solving
-24 + -2X + X2 = 11

Solving for variable 'X'.

Reorder the terms:
-24 + -11 + -2X + X2 = 11 + -11

Combine like terms: -24 + -11 = -35
-35 + -2X + X2 = 11 + -11

Combine like terms: 11 + -11 = 0
-35 + -2X + X2 = 0

Factor a trinomial.
(-5 + -1X)(7 + -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 '(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
Solution
X = {-5, 7}

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