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

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


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

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

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

Multiply (3 + x) * (-5 + 2x)
5(3(-5 + 2x) + x(-5 + 2x)) = 0
5((-5 * 3 + 2x * 3) + x(-5 + 2x)) = 0
5((-15 + 6x) + x(-5 + 2x)) = 0
5(-15 + 6x + (-5 * x + 2x * x)) = 0
5(-15 + 6x + (-5x + 2x2)) = 0

Combine like terms: 6x + -5x = 1x
5(-15 + 1x + 2x2) = 0
(-15 * 5 + 1x * 5 + 2x2 * 5) = 0
(-75 + 5x + 10x2) = 0

Solving
-75 + 5x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-15 + x + 2x2) = 0

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

Ignore the factor 5.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-3, 2.5}

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