(x-4)(x+5)=-18

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Solution for (x-4)(x+5)=-18 equation:


Simplifying
(x + -4)(x + 5) = -18

Reorder the terms:
(-4 + x)(x + 5) = -18

Reorder the terms:
(-4 + x)(5 + x) = -18

Multiply (-4 + x) * (5 + x)
(-4(5 + x) + x(5 + x)) = -18
((5 * -4 + x * -4) + x(5 + x)) = -18
((-20 + -4x) + x(5 + x)) = -18
(-20 + -4x + (5 * x + x * x)) = -18
(-20 + -4x + (5x + x2)) = -18

Combine like terms: -4x + 5x = 1x
(-20 + 1x + x2) = -18

Solving
-20 + 1x + x2 = -18

Solving for variable 'x'.

Reorder the terms:
-20 + 18 + 1x + x2 = -18 + 18

Combine like terms: -20 + 18 = -2
-2 + 1x + x2 = -18 + 18

Combine like terms: -18 + 18 = 0
-2 + 1x + x2 = 0

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

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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