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

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


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

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

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

Multiply (-2 + x) * (5 + x)
3(-2(5 + x) + x(5 + x)) = 0
3((5 * -2 + x * -2) + x(5 + x)) = 0
3((-10 + -2x) + x(5 + x)) = 0
3(-10 + -2x + (5 * x + x * x)) = 0
3(-10 + -2x + (5x + x2)) = 0

Combine like terms: -2x + 5x = 3x
3(-10 + 3x + x2) = 0
(-10 * 3 + 3x * 3 + x2 * 3) = 0
(-30 + 9x + 3x2) = 0

Solving
-30 + 9x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + 3x + x2) = 0

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

Ignore the factor 3.

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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-5, 2}

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