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

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


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

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

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

Multiply (-1 + 9x) * (9 + 6x)
(-1(9 + 6x) + 9x * (9 + 6x)) = 0
((9 * -1 + 6x * -1) + 9x * (9 + 6x)) = 0
((-9 + -6x) + 9x * (9 + 6x)) = 0
(-9 + -6x + (9 * 9x + 6x * 9x)) = 0
(-9 + -6x + (81x + 54x2)) = 0

Combine like terms: -6x + 81x = 75x
(-9 + 75x + 54x2) = 0

Solving
-9 + 75x + 54x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 25x + 18x2) = 0

Factor a trinomial.
3((-3 + -2x)(1 + -9x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5

Subproblem 2

Set the factor '(1 + -9x)' equal to zero and attempt to solve: Simplifying 1 + -9x = 0 Solving 1 + -9x = 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 + -9x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -9x = 0 + -1 -9x = 0 + -1 Combine like terms: 0 + -1 = -1 -9x = -1 Divide each side by '-9'. x = 0.1111111111 Simplifying x = 0.1111111111

Solution

x = {-1.5, 0.1111111111}

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