(4x-9)(9x+6)=0

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Solution for (4x-9)(9x+6)=0 equation:


Simplifying
(4x + -9)(9x + 6) = 0

Reorder the terms:
(-9 + 4x)(9x + 6) = 0

Reorder the terms:
(-9 + 4x)(6 + 9x) = 0

Multiply (-9 + 4x) * (6 + 9x)
(-9(6 + 9x) + 4x * (6 + 9x)) = 0
((6 * -9 + 9x * -9) + 4x * (6 + 9x)) = 0
((-54 + -81x) + 4x * (6 + 9x)) = 0
(-54 + -81x + (6 * 4x + 9x * 4x)) = 0
(-54 + -81x + (24x + 36x2)) = 0

Combine like terms: -81x + 24x = -57x
(-54 + -57x + 36x2) = 0

Solving
-54 + -57x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + -19x + 12x2) = 0

Factor a trinomial.
3((-2 + -3x)(9 + -4x)) = 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 '(9 + -4x)' equal to zero and attempt to solve: Simplifying 9 + -4x = 0 Solving 9 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4x = 0 + -9 -4x = 0 + -9 Combine like terms: 0 + -9 = -9 -4x = -9 Divide each side by '-4'. x = 2.25 Simplifying x = 2.25

Solution

x = {-0.6666666667, 2.25}

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