(x+4)(x-1)=-6

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Solution for (x+4)(x-1)=-6 equation:


Simplifying
(x + 4)(x + -1) = -6

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

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

Multiply (4 + x) * (-1 + x)
(4(-1 + x) + x(-1 + x)) = -6
((-1 * 4 + x * 4) + x(-1 + x)) = -6
((-4 + 4x) + x(-1 + x)) = -6
(-4 + 4x + (-1 * x + x * x)) = -6
(-4 + 4x + (-1x + x2)) = -6

Combine like terms: 4x + -1x = 3x
(-4 + 3x + x2) = -6

Solving
-4 + 3x + x2 = -6

Solving for variable 'x'.

Reorder the terms:
-4 + 6 + 3x + x2 = -6 + 6

Combine like terms: -4 + 6 = 2
2 + 3x + x2 = -6 + 6

Combine like terms: -6 + 6 = 0
2 + 3x + x2 = 0

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

Subproblem 1

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Subproblem 2

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

Solution

x = {-2, -1}

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