x(x+1)=5(x+(x+1))-5

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Solution for x(x+1)=5(x+(x+1))-5 equation:


Simplifying
x(x + 1) = 5(x + (x + 1)) + -5

Reorder the terms:
x(1 + x) = 5(x + (x + 1)) + -5
(1 * x + x * x) = 5(x + (x + 1)) + -5
(1x + x2) = 5(x + (x + 1)) + -5

Reorder the terms:
1x + x2 = 5(x + (1 + x)) + -5

Remove parenthesis around (1 + x)
1x + x2 = 5(x + 1 + x) + -5

Reorder the terms:
1x + x2 = 5(1 + x + x) + -5

Combine like terms: x + x = 2x
1x + x2 = 5(1 + 2x) + -5
1x + x2 = (1 * 5 + 2x * 5) + -5
1x + x2 = (5 + 10x) + -5

Reorder the terms:
1x + x2 = 5 + -5 + 10x

Combine like terms: 5 + -5 = 0
1x + x2 = 0 + 10x
1x + x2 = 10x

Solving
1x + x2 = 10x

Solving for variable 'x'.

Reorder the terms:
1x + -10x + x2 = 10x + -10x

Combine like terms: 1x + -10x = -9x
-9x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-9x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-9 + 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 '(-9 + x)' equal to zero and attempt to solve: Simplifying -9 + x = 0 Solving -9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0 + 9 x = 0 + 9 Combine like terms: 0 + 9 = 9 x = 9 Simplifying x = 9

Solution

x = {0, 9}

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