(2x-9)(x+2)=24

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Solution for (2x-9)(x+2)=24 equation:


Simplifying
(2x + -9)(x + 2) = 24

Reorder the terms:
(-9 + 2x)(x + 2) = 24

Reorder the terms:
(-9 + 2x)(2 + x) = 24

Multiply (-9 + 2x) * (2 + x)
(-9(2 + x) + 2x * (2 + x)) = 24
((2 * -9 + x * -9) + 2x * (2 + x)) = 24
((-18 + -9x) + 2x * (2 + x)) = 24
(-18 + -9x + (2 * 2x + x * 2x)) = 24
(-18 + -9x + (4x + 2x2)) = 24

Combine like terms: -9x + 4x = -5x
(-18 + -5x + 2x2) = 24

Solving
-18 + -5x + 2x2 = 24

Solving for variable 'x'.

Reorder the terms:
-18 + -24 + -5x + 2x2 = 24 + -24

Combine like terms: -18 + -24 = -42
-42 + -5x + 2x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-42 + -5x + 2x2 = 0

Factor a trinomial.
(-7 + -2x)(6 + -1x) = 0

Subproblem 1

Set the factor '(-7 + -2x)' equal to zero and attempt to solve: Simplifying -7 + -2x = 0 Solving -7 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2x = 0 + 7 -2x = 0 + 7 Combine like terms: 0 + 7 = 7 -2x = 7 Divide each side by '-2'. x = -3.5 Simplifying x = -3.5

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 = {-3.5, 6}

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