(24x-1)=(x+1)(x+2)(4)

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Solution for (24x-1)=(x+1)(x+2)(4) equation: 


Simplifying
(24x + -1) = (x + 1)(x + 2)(4)

Reorder the terms:
(-1 + 24x) = (x + 1)(x + 2)(4)

Remove parenthesis around (-1 + 24x)
-1 + 24x = (x + 1)(x + 2)(4)

Reorder the terms:
-1 + 24x = (1 + x)(x + 2)(4)

Reorder the terms:
-1 + 24x = (1 + x)(2 + x)(4)

Reorder the terms for easier multiplication:
-1 + 24x = 4(1 + x)(2 + x)

Multiply (1 + x) * (2 + x)
-1 + 24x = 4(1(2 + x) + x(2 + x))
-1 + 24x = 4((2 * 1 + x * 1) + x(2 + x))
-1 + 24x = 4((2 + 1x) + x(2 + x))
-1 + 24x = 4(2 + 1x + (2 * x + x * x))
-1 + 24x = 4(2 + 1x + (2x + x2))

Combine like terms: 1x + 2x = 3x
-1 + 24x = 4(2 + 3x + x2)
-1 + 24x = (2 * 4 + 3x * 4 + x2 * 4)
-1 + 24x = (8 + 12x + 4x2)

Solving
-1 + 24x = 8 + 12x + 4x2

Solving for variable 'x'.

Reorder the terms:
-1 + -8 + 24x + -12x + -4x2 = 8 + 12x + 4x2 + -8 + -12x + -4x2

Combine like terms: -1 + -8 = -9
-9 + 24x + -12x + -4x2 = 8 + 12x + 4x2 + -8 + -12x + -4x2

Combine like terms: 24x + -12x = 12x
-9 + 12x + -4x2 = 8 + 12x + 4x2 + -8 + -12x + -4x2

Reorder the terms:
-9 + 12x + -4x2 = 8 + -8 + 12x + -12x + 4x2 + -4x2

Combine like terms: 8 + -8 = 0
-9 + 12x + -4x2 = 0 + 12x + -12x + 4x2 + -4x2
-9 + 12x + -4x2 = 12x + -12x + 4x2 + -4x2

Combine like terms: 12x + -12x = 0
-9 + 12x + -4x2 = 0 + 4x2 + -4x2
-9 + 12x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-9 + 12x + -4x2 = 0

Factor a trinomial.
(-3 + 2x)(3 + -2x) = 0


Subproblem 1
Set the factor '(-3 + 2x)' equal to zero and attempt to solve:

Simplifying
-3 + 2x = 0

Solving
-3 + 2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + 2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2x = 0 + 3
2x = 0 + 3

Combine like terms: 0 + 3 = 3
2x = 3

Divide each side by '2'.
x = 1.5

Simplifying
x = 1.5

Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {1.5, 1.5}

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