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

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


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

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

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

Multiply (-2 + x) * (-7 + x)
-8(-2(-7 + x) + x(-7 + x)) = 0
-8((-7 * -2 + x * -2) + x(-7 + x)) = 0
-8((14 + -2x) + x(-7 + x)) = 0
-8(14 + -2x + (-7 * x + x * x)) = 0
-8(14 + -2x + (-7x + x2)) = 0

Combine like terms: -2x + -7x = -9x
-8(14 + -9x + x2) = 0
(14 * -8 + -9x * -8 + x2 * -8) = 0
(-112 + 72x + -8x2) = 0

Solving
-112 + 72x + -8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-14 + 9x + -1x2) = 0

Factor a trinomial.
8((-7 + x)(2 + -1x)) = 0

Ignore the factor 8.

Subproblem 1
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

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {7, 2}

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