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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