(x+2)(x-7)(3-8)=0

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Solution for (x+2)(x-7)(3-8)=0 equation: 


Simplifying
(x + 2)(x + -7)(3 + -8) = 0

Reorder the terms:
(2 + x)(x + -7)(3 + -8) = 0

Reorder the terms:
(2 + x)(-7 + x)(3 + -8) = 0

Combine like terms: 3 + -8 = -5
(2 + x)(-7 + x)(-5) = 0

Reorder the terms for easier multiplication:
-5(2 + x)(-7 + x) = 0

Multiply (2 + x) * (-7 + x)
-5(2(-7 + x) + x(-7 + x)) = 0
-5((-7 * 2 + x * 2) + x(-7 + x)) = 0
-5((-14 + 2x) + x(-7 + x)) = 0
-5(-14 + 2x + (-7 * x + x * x)) = 0
-5(-14 + 2x + (-7x + x2)) = 0

Combine like terms: 2x + -7x = -5x
-5(-14 + -5x + x2) = 0
(-14 * -5 + -5x * -5 + x2 * -5) = 0
(70 + 25x + -5x2) = 0

Solving
70 + 25x + -5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(14 + 5x + -1x2) = 0

Factor a trinomial.
5((7 + -1x)(2 + x)) = 0

Ignore the factor 5.

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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