(4x-32)(x+5)=0

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Solution for (4x-32)(x+5)=0 equation: 


Simplifying
(4x + -32)(x + 5) = 0

Reorder the terms:
(-32 + 4x)(x + 5) = 0

Reorder the terms:
(-32 + 4x)(5 + x) = 0

Multiply (-32 + 4x) * (5 + x)
(-32(5 + x) + 4x * (5 + x)) = 0
((5 * -32 + x * -32) + 4x * (5 + x)) = 0
((-160 + -32x) + 4x * (5 + x)) = 0
(-160 + -32x + (5 * 4x + x * 4x)) = 0
(-160 + -32x + (20x + 4x2)) = 0

Combine like terms: -32x + 20x = -12x
(-160 + -12x + 4x2) = 0

Solving
-160 + -12x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-40 + -3x + x2) = 0

Factor a trinomial.
4((-5 + -1x)(8 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

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 = {-5, 8}

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