(3x+5)(9x-5)=0

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Solution for (3x+5)(9x-5)=0 equation:


Simplifying
(3x + 5)(9x + -5) = 0

Reorder the terms:
(5 + 3x)(9x + -5) = 0

Reorder the terms:
(5 + 3x)(-5 + 9x) = 0

Multiply (5 + 3x) * (-5 + 9x)
(5(-5 + 9x) + 3x * (-5 + 9x)) = 0
((-5 * 5 + 9x * 5) + 3x * (-5 + 9x)) = 0
((-25 + 45x) + 3x * (-5 + 9x)) = 0
(-25 + 45x + (-5 * 3x + 9x * 3x)) = 0
(-25 + 45x + (-15x + 27x2)) = 0

Combine like terms: 45x + -15x = 30x
(-25 + 30x + 27x2) = 0

Solving
-25 + 30x + 27x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -3x)(5 + -9x) = 0

Subproblem 1

Set the factor '(-5 + -3x)' equal to zero and attempt to solve: Simplifying -5 + -3x = 0 Solving -5 + -3x = 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 + -3x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3x = 0 + 5 -3x = 0 + 5 Combine like terms: 0 + 5 = 5 -3x = 5 Divide each side by '-3'. x = -1.666666667 Simplifying x = -1.666666667

Subproblem 2

Set the factor '(5 + -9x)' equal to zero and attempt to solve: Simplifying 5 + -9x = 0 Solving 5 + -9x = 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 + -9x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9x = 0 + -5 -9x = 0 + -5 Combine like terms: 0 + -5 = -5 -9x = -5 Divide each side by '-9'. x = 0.5555555556 Simplifying x = 0.5555555556

Solution

x = {-1.666666667, 0.5555555556}

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