(x+5)(x-4)=x+16

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Solution for (x+5)(x-4)=x+16 equation:


Simplifying
(x + 5)(x + -4) = x + 16

Reorder the terms:
(5 + x)(x + -4) = x + 16

Reorder the terms:
(5 + x)(-4 + x) = x + 16

Multiply (5 + x) * (-4 + x)
(5(-4 + x) + x(-4 + x)) = x + 16
((-4 * 5 + x * 5) + x(-4 + x)) = x + 16
((-20 + 5x) + x(-4 + x)) = x + 16
(-20 + 5x + (-4 * x + x * x)) = x + 16
(-20 + 5x + (-4x + x2)) = x + 16

Combine like terms: 5x + -4x = 1x
(-20 + 1x + x2) = x + 16

Reorder the terms:
-20 + 1x + x2 = 16 + x

Solving
-20 + 1x + x2 = 16 + x

Solving for variable 'x'.

Reorder the terms:
-20 + -16 + 1x + -1x + x2 = 16 + x + -16 + -1x

Combine like terms: -20 + -16 = -36
-36 + 1x + -1x + x2 = 16 + x + -16 + -1x

Combine like terms: 1x + -1x = 0
-36 + 0 + x2 = 16 + x + -16 + -1x
-36 + x2 = 16 + x + -16 + -1x

Reorder the terms:
-36 + x2 = 16 + -16 + x + -1x

Combine like terms: 16 + -16 = 0
-36 + x2 = 0 + x + -1x
-36 + x2 = x + -1x

Combine like terms: x + -1x = 0
-36 + x2 = 0

Factor a difference between two squares.
(6 + x)(-6 + x) = 0

Subproblem 1

Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 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 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6

Subproblem 2

Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 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 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6

Solution

x = {-6, 6}

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