(2x-5)(x+1)=0

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Solution for (2x-5)(x+1)=0 equation:


Simplifying
(2x + -5)(x + 1) = 0

Reorder the terms:
(-5 + 2x)(x + 1) = 0

Reorder the terms:
(-5 + 2x)(1 + x) = 0

Multiply (-5 + 2x) * (1 + x)
(-5(1 + x) + 2x * (1 + x)) = 0
((1 * -5 + x * -5) + 2x * (1 + x)) = 0
((-5 + -5x) + 2x * (1 + x)) = 0
(-5 + -5x + (1 * 2x + x * 2x)) = 0
(-5 + -5x + (2x + 2x2)) = 0

Combine like terms: -5x + 2x = -3x
(-5 + -3x + 2x2) = 0

Solving
-5 + -3x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x)(5 + -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 '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Solution

x = {-1, 2.5}

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