(x+3)(x-5)=(2x+4)(x-5)

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Solution for (x+3)(x-5)=(2x+4)(x-5) equation:


Simplifying
(x + 3)(x + -5) = (2x + 4)(x + -5)

Reorder the terms:
(3 + x)(x + -5) = (2x + 4)(x + -5)

Reorder the terms:
(3 + x)(-5 + x) = (2x + 4)(x + -5)

Multiply (3 + x) * (-5 + x)
(3(-5 + x) + x(-5 + x)) = (2x + 4)(x + -5)
((-5 * 3 + x * 3) + x(-5 + x)) = (2x + 4)(x + -5)
((-15 + 3x) + x(-5 + x)) = (2x + 4)(x + -5)
(-15 + 3x + (-5 * x + x * x)) = (2x + 4)(x + -5)
(-15 + 3x + (-5x + x2)) = (2x + 4)(x + -5)

Combine like terms: 3x + -5x = -2x
(-15 + -2x + x2) = (2x + 4)(x + -5)

Reorder the terms:
-15 + -2x + x2 = (4 + 2x)(x + -5)

Reorder the terms:
-15 + -2x + x2 = (4 + 2x)(-5 + x)

Multiply (4 + 2x) * (-5 + x)
-15 + -2x + x2 = (4(-5 + x) + 2x * (-5 + x))
-15 + -2x + x2 = ((-5 * 4 + x * 4) + 2x * (-5 + x))
-15 + -2x + x2 = ((-20 + 4x) + 2x * (-5 + x))
-15 + -2x + x2 = (-20 + 4x + (-5 * 2x + x * 2x))
-15 + -2x + x2 = (-20 + 4x + (-10x + 2x2))

Combine like terms: 4x + -10x = -6x
-15 + -2x + x2 = (-20 + -6x + 2x2)

Solving
-15 + -2x + x2 = -20 + -6x + 2x2

Solving for variable 'x'.

Reorder the terms:
-15 + 20 + -2x + 6x + x2 + -2x2 = -20 + -6x + 2x2 + 20 + 6x + -2x2

Combine like terms: -15 + 20 = 5
5 + -2x + 6x + x2 + -2x2 = -20 + -6x + 2x2 + 20 + 6x + -2x2

Combine like terms: -2x + 6x = 4x
5 + 4x + x2 + -2x2 = -20 + -6x + 2x2 + 20 + 6x + -2x2

Combine like terms: x2 + -2x2 = -1x2
5 + 4x + -1x2 = -20 + -6x + 2x2 + 20 + 6x + -2x2

Reorder the terms:
5 + 4x + -1x2 = -20 + 20 + -6x + 6x + 2x2 + -2x2

Combine like terms: -20 + 20 = 0
5 + 4x + -1x2 = 0 + -6x + 6x + 2x2 + -2x2
5 + 4x + -1x2 = -6x + 6x + 2x2 + -2x2

Combine like terms: -6x + 6x = 0
5 + 4x + -1x2 = 0 + 2x2 + -2x2
5 + 4x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
5 + 4x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(1 + x) = 0

Subproblem 1

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

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 = {5, -1}

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