(x+1)(x-4)=36

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Solution for (x+1)(x-4)=36 equation:


Simplifying
(x + 1)(x + -4) = 36

Reorder the terms:
(1 + x)(x + -4) = 36

Reorder the terms:
(1 + x)(-4 + x) = 36

Multiply (1 + x) * (-4 + x)
(1(-4 + x) + x(-4 + x)) = 36
((-4 * 1 + x * 1) + x(-4 + x)) = 36
((-4 + 1x) + x(-4 + x)) = 36
(-4 + 1x + (-4 * x + x * x)) = 36
(-4 + 1x + (-4x + x2)) = 36

Combine like terms: 1x + -4x = -3x
(-4 + -3x + x2) = 36

Solving
-4 + -3x + x2 = 36

Solving for variable 'x'.

Reorder the terms:
-4 + -36 + -3x + x2 = 36 + -36

Combine like terms: -4 + -36 = -40
-40 + -3x + x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-40 + -3x + x2 = 0

Factor a trinomial.
(-5 + -1x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8

Solution

x = {-5, 8}

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