(x+3)(x-8)=26

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Solution for (x+3)(x-8)=26 equation:


Simplifying
(x + 3)(x + -8) = 26

Reorder the terms:
(3 + x)(x + -8) = 26

Reorder the terms:
(3 + x)(-8 + x) = 26

Multiply (3 + x) * (-8 + x)
(3(-8 + x) + x(-8 + x)) = 26
((-8 * 3 + x * 3) + x(-8 + x)) = 26
((-24 + 3x) + x(-8 + x)) = 26
(-24 + 3x + (-8 * x + x * x)) = 26
(-24 + 3x + (-8x + x2)) = 26

Combine like terms: 3x + -8x = -5x
(-24 + -5x + x2) = 26

Solving
-24 + -5x + x2 = 26

Solving for variable 'x'.

Reorder the terms:
-24 + -26 + -5x + x2 = 26 + -26

Combine like terms: -24 + -26 = -50
-50 + -5x + x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-50 + -5x + x2 = 0

Factor a trinomial.
(-5 + -1x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10

Solution

x = {-5, 10}

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