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

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


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

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

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

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

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

Reorder the terms:
-12 + -1x + x2 = (4 + 2x)(x + -4)

Reorder the terms:
-12 + -1x + x2 = (4 + 2x)(-4 + x)

Multiply (4 + 2x) * (-4 + x)
-12 + -1x + x2 = (4(-4 + x) + 2x * (-4 + x))
-12 + -1x + x2 = ((-4 * 4 + x * 4) + 2x * (-4 + x))
-12 + -1x + x2 = ((-16 + 4x) + 2x * (-4 + x))
-12 + -1x + x2 = (-16 + 4x + (-4 * 2x + x * 2x))
-12 + -1x + x2 = (-16 + 4x + (-8x + 2x2))

Combine like terms: 4x + -8x = -4x
-12 + -1x + x2 = (-16 + -4x + 2x2)

Solving
-12 + -1x + x2 = -16 + -4x + 2x2

Solving for variable 'x'.

Reorder the terms:
-12 + 16 + -1x + 4x + x2 + -2x2 = -16 + -4x + 2x2 + 16 + 4x + -2x2

Combine like terms: -12 + 16 = 4
4 + -1x + 4x + x2 + -2x2 = -16 + -4x + 2x2 + 16 + 4x + -2x2

Combine like terms: -1x + 4x = 3x
4 + 3x + x2 + -2x2 = -16 + -4x + 2x2 + 16 + 4x + -2x2

Combine like terms: x2 + -2x2 = -1x2
4 + 3x + -1x2 = -16 + -4x + 2x2 + 16 + 4x + -2x2

Reorder the terms:
4 + 3x + -1x2 = -16 + 16 + -4x + 4x + 2x2 + -2x2

Combine like terms: -16 + 16 = 0
4 + 3x + -1x2 = 0 + -4x + 4x + 2x2 + -2x2
4 + 3x + -1x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
4 + 3x + -1x2 = 0 + 2x2 + -2x2
4 + 3x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
4 + 3x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(1 + x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {4, -1}

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