0=(X-7)(X+2)

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Solution for 0=(X-7)(X+2) equation: 


Simplifying
0 = (X + -7)(X + 2)

Reorder the terms:
0 = (-7 + X)(X + 2)

Reorder the terms:
0 = (-7 + X)(2 + X)

Multiply (-7 + X) * (2 + X)
0 = (-7(2 + X) + X(2 + X))
0 = ((2 * -7 + X * -7) + X(2 + X))
0 = ((-14 + -7X) + X(2 + X))
0 = (-14 + -7X + (2 * X + X * X))
0 = (-14 + -7X + (2X + X2))

Combine like terms: -7X + 2X = -5X
0 = (-14 + -5X + X2)

Solving
0 = -14 + -5X + X2

Solving for variable 'X'.

Combine like terms: 0 + 14 = 14
14 + 5X + -1X2 = -14 + -5X + X2 + 14 + 5X + -1X2

Reorder the terms:
14 + 5X + -1X2 = -14 + 14 + -5X + 5X + X2 + -1X2

Combine like terms: -14 + 14 = 0
14 + 5X + -1X2 = 0 + -5X + 5X + X2 + -1X2
14 + 5X + -1X2 = -5X + 5X + X2 + -1X2

Combine like terms: -5X + 5X = 0
14 + 5X + -1X2 = 0 + X2 + -1X2
14 + 5X + -1X2 = X2 + -1X2

Combine like terms: X2 + -1X2 = 0
14 + 5X + -1X2 = 0

Factor a trinomial.
(7 + -1X)(2 + X) = 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 '(2 + X)' equal to zero and attempt to solve:

Simplifying
2 + X = 0

Solving
2 + X = 0

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

Add '-2' to each side of the equation.
2 + -2 + X = 0 + -2

Combine like terms: 2 + -2 = 0
0 + X = 0 + -2
X = 0 + -2

Combine like terms: 0 + -2 = -2
X = -2

Simplifying
X = -2
Solution
X = {7, -2}

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