5(x+1)(x-8)=0

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Solution for 5(x+1)(x-8)=0 equation: 


Simplifying
5(x + 1)(x + -8) = 0

Reorder the terms:
5(1 + x)(x + -8) = 0

Reorder the terms:
5(1 + x)(-8 + x) = 0

Multiply (1 + x) * (-8 + x)
5(1(-8 + x) + x(-8 + x)) = 0
5((-8 * 1 + x * 1) + x(-8 + x)) = 0
5((-8 + 1x) + x(-8 + x)) = 0
5(-8 + 1x + (-8 * x + x * x)) = 0
5(-8 + 1x + (-8x + x2)) = 0

Combine like terms: 1x + -8x = -7x
5(-8 + -7x + x2) = 0
(-8 * 5 + -7x * 5 + x2 * 5) = 0
(-40 + -35x + 5x2) = 0

Solving
-40 + -35x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-8 + -7x + x2) = 0

Factor a trinomial.
5((-1 + -1x)(8 + -1x)) = 0

Ignore the factor 5.

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-1, 8}

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