(2x+8)(2x+6)=168

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Solution for (2x+8)(2x+6)=168 equation:


Simplifying
(2x + 8)(2x + 6) = 168

Reorder the terms:
(8 + 2x)(2x + 6) = 168

Reorder the terms:
(8 + 2x)(6 + 2x) = 168

Multiply (8 + 2x) * (6 + 2x)
(8(6 + 2x) + 2x * (6 + 2x)) = 168
((6 * 8 + 2x * 8) + 2x * (6 + 2x)) = 168
((48 + 16x) + 2x * (6 + 2x)) = 168
(48 + 16x + (6 * 2x + 2x * 2x)) = 168
(48 + 16x + (12x + 4x2)) = 168

Combine like terms: 16x + 12x = 28x
(48 + 28x + 4x2) = 168

Solving
48 + 28x + 4x2 = 168

Solving for variable 'x'.

Reorder the terms:
48 + -168 + 28x + 4x2 = 168 + -168

Combine like terms: 48 + -168 = -120
-120 + 28x + 4x2 = 168 + -168

Combine like terms: 168 + -168 = 0
-120 + 28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-30 + 7x + x2) = 0

Factor a trinomial.
4((-10 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

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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