(x+1)(x-3)=12

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Solution for (x+1)(x-3)=12 equation:


Simplifying
(x + 1)(x + -3) = 12

Reorder the terms:
(1 + x)(x + -3) = 12

Reorder the terms:
(1 + x)(-3 + x) = 12

Multiply (1 + x) * (-3 + x)
(1(-3 + x) + x(-3 + x)) = 12
((-3 * 1 + x * 1) + x(-3 + x)) = 12
((-3 + 1x) + x(-3 + x)) = 12
(-3 + 1x + (-3 * x + x * x)) = 12
(-3 + 1x + (-3x + x2)) = 12

Combine like terms: 1x + -3x = -2x
(-3 + -2x + x2) = 12

Solving
-3 + -2x + x2 = 12

Solving for variable 'x'.

Reorder the terms:
-3 + -12 + -2x + x2 = 12 + -12

Combine like terms: -3 + -12 = -15
-15 + -2x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-15 + -2x + x2 = 0

Factor a trinomial.
(-3 + -1x)(5 + -1x) = 0

Subproblem 1

Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3

Subproblem 2

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

Solution

x = {-3, 5}

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