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

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


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

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

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

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

Combine like terms: 2x + -1x = 1x
5(-2 + 1x + x2) = 0
(-2 * 5 + 1x * 5 + x2 * 5) = 0
(-10 + 5x + 5x2) = 0

Solving
-10 + 5x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + x + x2) = 0

Factor a trinomial.
5((-2 + -1x)(1 + -1x)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2

Subproblem 2

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

Solution

x = {-2, 1}

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