(2x-6)(x+1)=0

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Solution for (2x-6)(x+1)=0 equation:


Simplifying
(2x + -6)(x + 1) = 0

Reorder the terms:
(-6 + 2x)(x + 1) = 0

Reorder the terms:
(-6 + 2x)(1 + x) = 0

Multiply (-6 + 2x) * (1 + x)
(-6(1 + x) + 2x * (1 + x)) = 0
((1 * -6 + x * -6) + 2x * (1 + x)) = 0
((-6 + -6x) + 2x * (1 + x)) = 0
(-6 + -6x + (1 * 2x + x * 2x)) = 0
(-6 + -6x + (2x + 2x2)) = 0

Combine like terms: -6x + 2x = -4x
(-6 + -4x + 2x2) = 0

Solving
-6 + -4x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -2x + x2) = 0

Factor a trinomial.
2((-1 + -1x)(3 + -1x)) = 0

Ignore the factor 2.

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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-1, 3}

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