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

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


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

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

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

Multiply (-3 + x) * (8 + 5x)
2(-3(8 + 5x) + x(8 + 5x)) = 0
2((8 * -3 + 5x * -3) + x(8 + 5x)) = 0
2((-24 + -15x) + x(8 + 5x)) = 0
2(-24 + -15x + (8 * x + 5x * x)) = 0
2(-24 + -15x + (8x + 5x2)) = 0

Combine like terms: -15x + 8x = -7x
2(-24 + -7x + 5x2) = 0
(-24 * 2 + -7x * 2 + 5x2 * 2) = 0
(-48 + -14x + 10x2) = 0

Solving
-48 + -14x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + -7x + 5x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + -5x)' equal to zero and attempt to solve:

Simplifying
-8 + -5x = 0

Solving
-8 + -5x = 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 + -5x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5x = 0 + 8
-5x = 0 + 8

Combine like terms: 0 + 8 = 8
-5x = 8

Divide each side by '-5'.
x = -1.6

Simplifying
x = -1.6

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1.6, 3}

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