(2x+9)(x-6)=0

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Solution for (2x+9)(x-6)=0 equation:


Simplifying
(2x + 9)(x + -6) = 0

Reorder the terms:
(9 + 2x)(x + -6) = 0

Reorder the terms:
(9 + 2x)(-6 + x) = 0

Multiply (9 + 2x) * (-6 + x)
(9(-6 + x) + 2x * (-6 + x)) = 0
((-6 * 9 + x * 9) + 2x * (-6 + x)) = 0
((-54 + 9x) + 2x * (-6 + x)) = 0
(-54 + 9x + (-6 * 2x + x * 2x)) = 0
(-54 + 9x + (-12x + 2x2)) = 0

Combine like terms: 9x + -12x = -3x
(-54 + -3x + 2x2) = 0

Solving
-54 + -3x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + -2x)(6 + -1x) = 0

Subproblem 1

Set the factor '(-9 + -2x)' equal to zero and attempt to solve: Simplifying -9 + -2x = 0 Solving -9 + -2x = 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 + -2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2x = 0 + 9 -2x = 0 + 9 Combine like terms: 0 + 9 = 9 -2x = 9 Divide each side by '-2'. x = -4.5 Simplifying x = -4.5

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {-4.5, 6}

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