3(2x+5)(x-8)=0

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Solution for 3(2x+5)(x-8)=0 equation: 


Simplifying
3(2x + 5)(x + -8) = 0

Reorder the terms:
3(5 + 2x)(x + -8) = 0

Reorder the terms:
3(5 + 2x)(-8 + x) = 0

Multiply (5 + 2x) * (-8 + x)
3(5(-8 + x) + 2x * (-8 + x)) = 0
3((-8 * 5 + x * 5) + 2x * (-8 + x)) = 0
3((-40 + 5x) + 2x * (-8 + x)) = 0
3(-40 + 5x + (-8 * 2x + x * 2x)) = 0
3(-40 + 5x + (-16x + 2x2)) = 0

Combine like terms: 5x + -16x = -11x
3(-40 + -11x + 2x2) = 0
(-40 * 3 + -11x * 3 + 2x2 * 3) = 0
(-120 + -33x + 6x2) = 0

Solving
-120 + -33x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-40 + -11x + 2x2) = 0

Factor a trinomial.
3((-5 + -2x)(8 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

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 = {-2.5, 8}

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