(5x-1)(9x+6)=0

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Solution for (5x-1)(9x+6)=0 equation:


Simplifying
(5x + -1)(9x + 6) = 0

Reorder the terms:
(-1 + 5x)(9x + 6) = 0

Reorder the terms:
(-1 + 5x)(6 + 9x) = 0

Multiply (-1 + 5x) * (6 + 9x)
(-1(6 + 9x) + 5x * (6 + 9x)) = 0
((6 * -1 + 9x * -1) + 5x * (6 + 9x)) = 0
((-6 + -9x) + 5x * (6 + 9x)) = 0
(-6 + -9x + (6 * 5x + 9x * 5x)) = 0
(-6 + -9x + (30x + 45x2)) = 0

Combine like terms: -9x + 30x = 21x
(-6 + 21x + 45x2) = 0

Solving
-6 + 21x + 45x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 7x + 15x2) = 0

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

Ignore the factor 3.

Subproblem 1

Set the factor '(-2 + -3x)' equal to zero and attempt to solve: Simplifying -2 + -3x = 0 Solving -2 + -3x = 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 + -3x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3x = 0 + 2 -3x = 0 + 2 Combine like terms: 0 + 2 = 2 -3x = 2 Divide each side by '-3'. x = -0.6666666667 Simplifying x = -0.6666666667

Subproblem 2

Set the factor '(1 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2

Solution

x = {-0.6666666667, 0.2}

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