(2x-3)(x+9)=0

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Solution for (2x-3)(x+9)=0 equation:


Simplifying
(2x + -3)(x + 9) = 0

Reorder the terms:
(-3 + 2x)(x + 9) = 0

Reorder the terms:
(-3 + 2x)(9 + x) = 0

Multiply (-3 + 2x) * (9 + x)
(-3(9 + x) + 2x * (9 + x)) = 0
((9 * -3 + x * -3) + 2x * (9 + x)) = 0
((-27 + -3x) + 2x * (9 + x)) = 0
(-27 + -3x + (9 * 2x + x * 2x)) = 0
(-27 + -3x + (18x + 2x2)) = 0

Combine like terms: -3x + 18x = 15x
(-27 + 15x + 2x2) = 0

Solving
-27 + 15x + 2x2 = 0

Solving for variable 'x'.

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

Subproblem 1

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

Subproblem 2

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

Solution

x = {-9, 1.5}

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