0=(x-3)(x+7)

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Solution for 0=(x-3)(x+7) equation:


Simplifying
0 = (x + -3)(x + 7)

Reorder the terms:
0 = (-3 + x)(x + 7)

Reorder the terms:
0 = (-3 + x)(7 + x)

Multiply (-3 + x) * (7 + x)
0 = (-3(7 + x) + x(7 + x))
0 = ((7 * -3 + x * -3) + x(7 + x))
0 = ((-21 + -3x) + x(7 + x))
0 = (-21 + -3x + (7 * x + x * x))
0 = (-21 + -3x + (7x + x2))

Combine like terms: -3x + 7x = 4x
0 = (-21 + 4x + x2)

Solving
0 = -21 + 4x + x2

Solving for variable 'x'.

Combine like terms: 0 + 21 = 21
21 + -4x + -1x2 = -21 + 4x + x2 + 21 + -4x + -1x2

Reorder the terms:
21 + -4x + -1x2 = -21 + 21 + 4x + -4x + x2 + -1x2

Combine like terms: -21 + 21 = 0
21 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2
21 + -4x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
21 + -4x + -1x2 = 0 + x2 + -1x2
21 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
21 + -4x + -1x2 = 0

Factor a trinomial.
(3 + -1x)(7 + x) = 0


Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 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 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {3, -7}

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