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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solving
4x + x2 = -9x + 2x2

Solving for variable 'x'.

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

Combine like terms: 4x + 9x = 13x
13x + x2 + -2x2 = -9x + 2x2 + 9x + -2x2

Combine like terms: x2 + -2x2 = -1x2
13x + -1x2 = -9x + 2x2 + 9x + -2x2

Reorder the terms:
13x + -1x2 = -9x + 9x + 2x2 + -2x2

Combine like terms: -9x + 9x = 0
13x + -1x2 = 0 + 2x2 + -2x2
13x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
13x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(13 + -1x) = 0

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 '(13 + -1x)' equal to zero and attempt to solve: Simplifying 13 + -1x = 0 Solving 13 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x = 0 + -13 -1x = 0 + -13 Combine like terms: 0 + -13 = -13 -1x = -13 Divide each side by '-1'. x = 13 Simplifying x = 13

Solution

x = {0, 13}

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