(2x-3)(x+4)=6

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Solution for (2x-3)(x+4)=6 equation: 


Simplifying
(2x + -3)(x + 4) = 6

Reorder the terms:
(-3 + 2x)(x + 4) = 6

Reorder the terms:
(-3 + 2x)(4 + x) = 6

Multiply (-3 + 2x) * (4 + x)
(-3(4 + x) + 2x * (4 + x)) = 6
((4 * -3 + x * -3) + 2x * (4 + x)) = 6
((-12 + -3x) + 2x * (4 + x)) = 6
(-12 + -3x + (4 * 2x + x * 2x)) = 6
(-12 + -3x + (8x + 2x2)) = 6

Combine like terms: -3x + 8x = 5x
(-12 + 5x + 2x2) = 6

Solving
-12 + 5x + 2x2 = 6

Solving for variable 'x'.

Reorder the terms:
-12 + -6 + 5x + 2x2 = 6 + -6

Combine like terms: -12 + -6 = -18
-18 + 5x + 2x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-18 + 5x + 2x2 = 0

Factor a trinomial.
(-9 + -2x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-4.5, 2}

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