(2x+6)(2x+8)=48+72

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Solution for (2x+6)(2x+8)=48+72 equation:


Simplifying
(2x + 6)(2x + 8) = 48 + 72

Reorder the terms:
(6 + 2x)(2x + 8) = 48 + 72

Reorder the terms:
(6 + 2x)(8 + 2x) = 48 + 72

Multiply (6 + 2x) * (8 + 2x)
(6(8 + 2x) + 2x * (8 + 2x)) = 48 + 72
((8 * 6 + 2x * 6) + 2x * (8 + 2x)) = 48 + 72
((48 + 12x) + 2x * (8 + 2x)) = 48 + 72
(48 + 12x + (8 * 2x + 2x * 2x)) = 48 + 72
(48 + 12x + (16x + 4x2)) = 48 + 72

Combine like terms: 12x + 16x = 28x
(48 + 28x + 4x2) = 48 + 72

Combine like terms: 48 + 72 = 120
48 + 28x + 4x2 = 120

Solving
48 + 28x + 4x2 = 120

Solving for variable 'x'.

Reorder the terms:
48 + -120 + 28x + 4x2 = 120 + -120

Combine like terms: 48 + -120 = -72
-72 + 28x + 4x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-72 + 28x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + 7x + x2) = 0

Factor a trinomial.
4((-9 + -1x)(2 + -1x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {-9, 2}

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