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

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


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

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

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

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

Combine like terms: 4x + -9x = -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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