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

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


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

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

Remove parenthesis around (-5 + x)
-5 + x + 10 = (x + 5)(x + -5)

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

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

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

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

Multiply (5 + x) * (-5 + x)
5 + x = (5(-5 + x) + x(-5 + x))
5 + x = ((-5 * 5 + x * 5) + x(-5 + x))
5 + x = ((-25 + 5x) + x(-5 + x))
5 + x = (-25 + 5x + (-5 * x + x * x))
5 + x = (-25 + 5x + (-5x + x2))

Combine like terms: 5x + -5x = 0
5 + x = (-25 + 0 + x2)
5 + x = (-25 + x2)

Solving
5 + x = -25 + x2

Solving for variable 'x'.

Reorder the terms:
5 + 25 + x + -1x2 = -25 + x2 + 25 + -1x2

Combine like terms: 5 + 25 = 30
30 + x + -1x2 = -25 + x2 + 25 + -1x2

Reorder the terms:
30 + x + -1x2 = -25 + 25 + x2 + -1x2

Combine like terms: -25 + 25 = 0
30 + x + -1x2 = 0 + x2 + -1x2
30 + x + -1x2 = x2 + -1x2

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

Factor a trinomial.
(6 + -1x)(5 + x) = 0

Subproblem 1

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Subproblem 2

Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5

Solution

x = {6, -5}

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