-18x=(2x-3)(x+4)

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Solution for -18x=(2x-3)(x+4) equation: 


Simplifying
-18x = (2x + -3)(x + 4)

Reorder the terms:
-18x = (-3 + 2x)(x + 4)

Reorder the terms:
-18x = (-3 + 2x)(4 + x)

Multiply (-3 + 2x) * (4 + x)
-18x = (-3(4 + x) + 2x * (4 + x))
-18x = ((4 * -3 + x * -3) + 2x * (4 + x))
-18x = ((-12 + -3x) + 2x * (4 + x))
-18x = (-12 + -3x + (4 * 2x + x * 2x))
-18x = (-12 + -3x + (8x + 2x2))

Combine like terms: -3x + 8x = 5x
-18x = (-12 + 5x + 2x2)

Solving
-18x = -12 + 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
12 + -18x + -5x + -2x2 = -12 + 5x + 2x2 + 12 + -5x + -2x2

Combine like terms: -18x + -5x = -23x
12 + -23x + -2x2 = -12 + 5x + 2x2 + 12 + -5x + -2x2

Reorder the terms:
12 + -23x + -2x2 = -12 + 12 + 5x + -5x + 2x2 + -2x2

Combine like terms: -12 + 12 = 0
12 + -23x + -2x2 = 0 + 5x + -5x + 2x2 + -2x2
12 + -23x + -2x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
12 + -23x + -2x2 = 0 + 2x2 + -2x2
12 + -23x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
12 + -23x + -2x2 = 0

Factor a trinomial.
(1 + -2x)(12 + x) = 0


Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Solution
x = {0.5, -12}

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