(x-5)(2x+4)=(x+10)(x-2)

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Solution for (x-5)(2x+4)=(x+10)(x-2) equation:


Simplifying
(x + -5)(2x + 4) = (x + 10)(x + -2)

Reorder the terms:
(-5 + x)(2x + 4) = (x + 10)(x + -2)

Reorder the terms:
(-5 + x)(4 + 2x) = (x + 10)(x + -2)

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

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

Reorder the terms:
-20 + -6x + 2x2 = (10 + x)(x + -2)

Reorder the terms:
-20 + -6x + 2x2 = (10 + x)(-2 + x)

Multiply (10 + x) * (-2 + x)
-20 + -6x + 2x2 = (10(-2 + x) + x(-2 + x))
-20 + -6x + 2x2 = ((-2 * 10 + x * 10) + x(-2 + x))
-20 + -6x + 2x2 = ((-20 + 10x) + x(-2 + x))
-20 + -6x + 2x2 = (-20 + 10x + (-2 * x + x * x))
-20 + -6x + 2x2 = (-20 + 10x + (-2x + x2))

Combine like terms: 10x + -2x = 8x
-20 + -6x + 2x2 = (-20 + 8x + x2)

Add '20' to each side of the equation.
-20 + -6x + 20 + 2x2 = -20 + 8x + 20 + x2

Reorder the terms:
-20 + 20 + -6x + 2x2 = -20 + 8x + 20 + x2

Combine like terms: -20 + 20 = 0
0 + -6x + 2x2 = -20 + 8x + 20 + x2
-6x + 2x2 = -20 + 8x + 20 + x2

Reorder the terms:
-6x + 2x2 = -20 + 20 + 8x + x2

Combine like terms: -20 + 20 = 0
-6x + 2x2 = 0 + 8x + x2
-6x + 2x2 = 8x + x2

Solving
-6x + 2x2 = 8x + x2

Solving for variable 'x'.

Reorder the terms:
-6x + -8x + 2x2 + -1x2 = 8x + x2 + -8x + -1x2

Combine like terms: -6x + -8x = -14x
-14x + 2x2 + -1x2 = 8x + x2 + -8x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-14x + 1x2 = 8x + x2 + -8x + -1x2

Reorder the terms:
-14x + 1x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
-14x + 1x2 = 0 + x2 + -1x2
-14x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-14x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-14 + x) = 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 '(-14 + x)' equal to zero and attempt to solve: Simplifying -14 + x = 0 Solving -14 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 0 + 14 Combine like terms: -14 + 14 = 0 0 + x = 0 + 14 x = 0 + 14 Combine like terms: 0 + 14 = 14 x = 14 Simplifying x = 14

Solution

x = {0, 14}

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