(2x+8)(x+3)(.5)=42

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Solution for (2x+8)(x+3)(.5)=42 equation:


Simplifying
(2x + 8)(x + 3)(0.5) = 42

Reorder the terms:
(8 + 2x)(x + 3)(0.5) = 42

Reorder the terms:
(8 + 2x)(3 + x)(0.5) = 42

Reorder the terms for easier multiplication:
0.5(8 + 2x)(3 + x) = 42

Multiply (8 + 2x) * (3 + x)
0.5(8(3 + x) + 2x * (3 + x)) = 42
0.5((3 * 8 + x * 8) + 2x * (3 + x)) = 42
0.5((24 + 8x) + 2x * (3 + x)) = 42
0.5(24 + 8x + (3 * 2x + x * 2x)) = 42
0.5(24 + 8x + (6x + 2x2)) = 42

Combine like terms: 8x + 6x = 14x
0.5(24 + 14x + 2x2) = 42
(24 * 0.5 + 14x * 0.5 + 2x2 * 0.5) = 42
(12 + 7x + 1x2) = 42

Solving
12 + 7x + 1x2 = 42

Solving for variable 'x'.

Reorder the terms:
12 + -42 + 7x + 1x2 = 42 + -42

Combine like terms: 12 + -42 = -30
-30 + 7x + 1x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-30 + 7x + 1x2 = 0

Factor a trinomial.
(-10 + -1x)(3 + -1x) = 0

Subproblem 1

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

Subproblem 2

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

Solution

x = {-10, 3}

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