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

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


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

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

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

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

Combine like terms: -10x + 2x = -8x
(-10 + -8x + 2x2) = (x + 5)(x + -2)

Reorder the terms:
-10 + -8x + 2x2 = (5 + x)(x + -2)

Reorder the terms:
-10 + -8x + 2x2 = (5 + x)(-2 + x)

Multiply (5 + x) * (-2 + x)
-10 + -8x + 2x2 = (5(-2 + x) + x(-2 + x))
-10 + -8x + 2x2 = ((-2 * 5 + x * 5) + x(-2 + x))
-10 + -8x + 2x2 = ((-10 + 5x) + x(-2 + x))
-10 + -8x + 2x2 = (-10 + 5x + (-2 * x + x * x))
-10 + -8x + 2x2 = (-10 + 5x + (-2x + x2))

Combine like terms: 5x + -2x = 3x
-10 + -8x + 2x2 = (-10 + 3x + x2)

Add '10' to each side of the equation.
-10 + -8x + 10 + 2x2 = -10 + 3x + 10 + x2

Reorder the terms:
-10 + 10 + -8x + 2x2 = -10 + 3x + 10 + x2

Combine like terms: -10 + 10 = 0
0 + -8x + 2x2 = -10 + 3x + 10 + x2
-8x + 2x2 = -10 + 3x + 10 + x2

Reorder the terms:
-8x + 2x2 = -10 + 10 + 3x + x2

Combine like terms: -10 + 10 = 0
-8x + 2x2 = 0 + 3x + x2
-8x + 2x2 = 3x + x2

Solving
-8x + 2x2 = 3x + x2

Solving for variable 'x'.

Reorder the terms:
-8x + -3x + 2x2 + -1x2 = 3x + x2 + -3x + -1x2

Combine like terms: -8x + -3x = -11x
-11x + 2x2 + -1x2 = 3x + x2 + -3x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-11x + 1x2 = 3x + x2 + -3x + -1x2

Reorder the terms:
-11x + 1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
-11x + 1x2 = 0 + x2 + -1x2
-11x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-11x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-11 + 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 '(-11 + x)' equal to zero and attempt to solve: Simplifying -11 + x = 0 Solving -11 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + x = 0 + 11 x = 0 + 11 Combine like terms: 0 + 11 = 11 x = 11 Simplifying x = 11

Solution

x = {0, 11}

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