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

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


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

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

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

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

Combine like terms: 2x + 1x = 3x
(2 + 3x + x2) = (4x + -1)(x + -2)

Reorder the terms:
2 + 3x + x2 = (-1 + 4x)(x + -2)

Reorder the terms:
2 + 3x + x2 = (-1 + 4x)(-2 + x)

Multiply (-1 + 4x) * (-2 + x)
2 + 3x + x2 = (-1(-2 + x) + 4x * (-2 + x))
2 + 3x + x2 = ((-2 * -1 + x * -1) + 4x * (-2 + x))
2 + 3x + x2 = ((2 + -1x) + 4x * (-2 + x))
2 + 3x + x2 = (2 + -1x + (-2 * 4x + x * 4x))
2 + 3x + x2 = (2 + -1x + (-8x + 4x2))

Combine like terms: -1x + -8x = -9x
2 + 3x + x2 = (2 + -9x + 4x2)

Add '-2' to each side of the equation.
2 + 3x + -2 + x2 = 2 + -9x + -2 + 4x2

Reorder the terms:
2 + -2 + 3x + x2 = 2 + -9x + -2 + 4x2

Combine like terms: 2 + -2 = 0
0 + 3x + x2 = 2 + -9x + -2 + 4x2
3x + x2 = 2 + -9x + -2 + 4x2

Reorder the terms:
3x + x2 = 2 + -2 + -9x + 4x2

Combine like terms: 2 + -2 = 0
3x + x2 = 0 + -9x + 4x2
3x + x2 = -9x + 4x2

Solving
3x + x2 = -9x + 4x2

Solving for variable 'x'.

Reorder the terms:
3x + 9x + x2 + -4x2 = -9x + 4x2 + 9x + -4x2

Combine like terms: 3x + 9x = 12x
12x + x2 + -4x2 = -9x + 4x2 + 9x + -4x2

Combine like terms: x2 + -4x2 = -3x2
12x + -3x2 = -9x + 4x2 + 9x + -4x2

Reorder the terms:
12x + -3x2 = -9x + 9x + 4x2 + -4x2

Combine like terms: -9x + 9x = 0
12x + -3x2 = 0 + 4x2 + -4x2
12x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
12x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(4 + -1x) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, 4}

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