(x-3)(x+5)=9

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Solution for (x-3)(x+5)=9 equation:


Simplifying
(x + -3)(x + 5) = 9

Reorder the terms:
(-3 + x)(x + 5) = 9

Reorder the terms:
(-3 + x)(5 + x) = 9

Multiply (-3 + x) * (5 + x)
(-3(5 + x) + x(5 + x)) = 9
((5 * -3 + x * -3) + x(5 + x)) = 9
((-15 + -3x) + x(5 + x)) = 9
(-15 + -3x + (5 * x + x * x)) = 9
(-15 + -3x + (5x + x2)) = 9

Combine like terms: -3x + 5x = 2x
(-15 + 2x + x2) = 9

Solving
-15 + 2x + x2 = 9

Solving for variable 'x'.

Reorder the terms:
-15 + -9 + 2x + x2 = 9 + -9

Combine like terms: -15 + -9 = -24
-24 + 2x + x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-24 + 2x + x2 = 0

Factor a trinomial.
(-6 + -1x)(4 + -1x) = 0

Subproblem 1

Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-6, 4}

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