(x+2)(x+1)*4=24

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Solution for (x+2)(x+1)*4=24 equation:


Simplifying
(x + 2)(x + 1) * 4 = 24

Reorder the terms:
(2 + x)(x + 1) * 4 = 24

Reorder the terms:
(2 + x)(1 + x) * 4 = 24

Reorder the terms for easier multiplication:
4(2 + x)(1 + x) = 24

Multiply (2 + x) * (1 + x)
4(2(1 + x) + x(1 + x)) = 24
4((1 * 2 + x * 2) + x(1 + x)) = 24
4((2 + 2x) + x(1 + x)) = 24
4(2 + 2x + (1 * x + x * x)) = 24
4(2 + 2x + (1x + x2)) = 24

Combine like terms: 2x + 1x = 3x
4(2 + 3x + x2) = 24
(2 * 4 + 3x * 4 + x2 * 4) = 24
(8 + 12x + 4x2) = 24

Solving
8 + 12x + 4x2 = 24

Solving for variable 'x'.

Reorder the terms:
8 + -24 + 12x + 4x2 = 24 + -24

Combine like terms: 8 + -24 = -16
-16 + 12x + 4x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-16 + 12x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 3x + x2) = 0

Factor a trinomial.
4((-4 + -1x)(1 + -1x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4

Subproblem 2

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

Solution

x = {-4, 1}

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