(X-3)(X+6)-10=0

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Solution for (X-3)(X+6)-10=0 equation: 


Simplifying
(X + -3)(X + 6) + -10 = 0

Reorder the terms:
(-3 + X)(X + 6) + -10 = 0

Reorder the terms:
(-3 + X)(6 + X) + -10 = 0

Multiply (-3 + X) * (6 + X)
(-3(6 + X) + X(6 + X)) + -10 = 0
((6 * -3 + X * -3) + X(6 + X)) + -10 = 0
((-18 + -3X) + X(6 + X)) + -10 = 0
(-18 + -3X + (6 * X + X * X)) + -10 = 0
(-18 + -3X + (6X + X2)) + -10 = 0

Combine like terms: -3X + 6X = 3X
(-18 + 3X + X2) + -10 = 0

Reorder the terms:
-18 + -10 + 3X + X2 = 0

Combine like terms: -18 + -10 = -28
-28 + 3X + X2 = 0

Solving
-28 + 3X + X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(-7 + -1X)(4 + -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 '(4 + -1X)' equal to zero and attempt to solve:

Simplifying
4 + -1X = 0

Solving
4 + -1X = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1X = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1X = 0 + -4
-1X = 0 + -4

Combine like terms: 0 + -4 = -4
-1X = -4

Divide each side by '-1'.
X = 4

Simplifying
X = 4
Solution
X = {-7, 4}

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