(x)(x-7)(x-12)=0

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Solution for (x)(x-7)(x-12)=0 equation: 


Simplifying
(x)(x + -7)(x + -12) = 0

Reorder the terms:
x(-7 + x)(x + -12) = 0

Reorder the terms:
x(-7 + x)(-12 + x) = 0

Multiply (-7 + x) * (-12 + x)
x(-7(-12 + x) + x(-12 + x)) = 0
x((-12 * -7 + x * -7) + x(-12 + x)) = 0
x((84 + -7x) + x(-12 + x)) = 0
x(84 + -7x + (-12 * x + x * x)) = 0
x(84 + -7x + (-12x + x2)) = 0

Combine like terms: -7x + -12x = -19x
x(84 + -19x + x2) = 0
(84 * x + -19x * x + x2 * x) = 0
(84x + -19x2 + x3) = 0

Solving
84x + -19x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(84 + -19x + x2) = 0

Factor a trinomial.
x((7 + -1x)(12 + -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 '(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 3
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {0, 7, 12}

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