(x-7)(x+3)=24

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Solution for (x-7)(x+3)=24 equation:


Simplifying
(x + -7)(x + 3) = 24

Reorder the terms:
(-7 + x)(x + 3) = 24

Reorder the terms:
(-7 + x)(3 + x) = 24

Multiply (-7 + x) * (3 + x)
(-7(3 + x) + x(3 + x)) = 24
((3 * -7 + x * -7) + x(3 + x)) = 24
((-21 + -7x) + x(3 + x)) = 24
(-21 + -7x + (3 * x + x * x)) = 24
(-21 + -7x + (3x + x2)) = 24

Combine like terms: -7x + 3x = -4x
(-21 + -4x + x2) = 24

Solving
-21 + -4x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
-21 + -24 + -4x + x2 = 24 + -24

Combine like terms: -21 + -24 = -45
-45 + -4x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-45 + -4x + x2 = 0

Factor a trinomial.
(-5 + -1x)(9 + -1x) = 0

Subproblem 1

Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5

Subproblem 2

Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9

Solution

x = {-5, 9}

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