2x(x+1)-(x+1)=0

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Solution for 2x(x+1)-(x+1)=0 equation:


Simplifying
2x(x + 1) + -1(x + 1) = 0

Reorder the terms:
2x(1 + x) + -1(x + 1) = 0
(1 * 2x + x * 2x) + -1(x + 1) = 0
(2x + 2x2) + -1(x + 1) = 0

Reorder the terms:
2x + 2x2 + -1(1 + x) = 0
2x + 2x2 + (1 * -1 + x * -1) = 0
2x + 2x2 + (-1 + -1x) = 0

Reorder the terms:
-1 + 2x + -1x + 2x2 = 0

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

Solving
-1 + 1x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x)(1 + -2x) = 0

Subproblem 1

Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1

Subproblem 2

Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

Solution

x = {-1, 0.5}

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