12(x-8)(4x+5)=0

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Solution for 12(x-8)(4x+5)=0 equation: 


Simplifying
12(x + -8)(4x + 5) = 0

Reorder the terms:
12(-8 + x)(4x + 5) = 0

Reorder the terms:
12(-8 + x)(5 + 4x) = 0

Multiply (-8 + x) * (5 + 4x)
12(-8(5 + 4x) + x(5 + 4x)) = 0
12((5 * -8 + 4x * -8) + x(5 + 4x)) = 0
12((-40 + -32x) + x(5 + 4x)) = 0
12(-40 + -32x + (5 * x + 4x * x)) = 0
12(-40 + -32x + (5x + 4x2)) = 0

Combine like terms: -32x + 5x = -27x
12(-40 + -27x + 4x2) = 0
(-40 * 12 + -27x * 12 + 4x2 * 12) = 0
(-480 + -324x + 48x2) = 0

Solving
-480 + -324x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-40 + -27x + 4x2) = 0

Factor a trinomial.
12((-5 + -4x)(8 + -1x)) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve:

Simplifying
-5 + -4x = 0

Solving
-5 + -4x = 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 + -4x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4x = 0 + 5
-4x = 0 + 5

Combine like terms: 0 + 5 = 5
-4x = 5

Divide each side by '-4'.
x = -1.25

Simplifying
x = -1.25

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 = {-1.25, 8}

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