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

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


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

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

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

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

Combine like terms: -3x + 5x = 2x
2(-15 + 2x + x2) = 0
(-15 * 2 + 2x * 2 + x2 * 2) = 0
(-30 + 4x + 2x2) = 0

Solving
-30 + 4x + 2x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 2.

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 '(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 = {-5, 3}

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