(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.
(-2 + -1x)(9 + -2x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-2, 4.5}

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