(3x+2)(7x+4)=8

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Solution for (3x+2)(7x+4)=8 equation: 


Simplifying
(3x + 2)(7x + 4) = 8

Reorder the terms:
(2 + 3x)(7x + 4) = 8

Reorder the terms:
(2 + 3x)(4 + 7x) = 8

Multiply (2 + 3x) * (4 + 7x)
(2(4 + 7x) + 3x * (4 + 7x)) = 8
((4 * 2 + 7x * 2) + 3x * (4 + 7x)) = 8
((8 + 14x) + 3x * (4 + 7x)) = 8
(8 + 14x + (4 * 3x + 7x * 3x)) = 8
(8 + 14x + (12x + 21x2)) = 8

Combine like terms: 14x + 12x = 26x
(8 + 26x + 21x2) = 8

Add '-8' to each side of the equation.
8 + 26x + -8 + 21x2 = 8 + -8

Reorder the terms:
8 + -8 + 26x + 21x2 = 8 + -8

Combine like terms: 8 + -8 = 0
0 + 26x + 21x2 = 8 + -8
26x + 21x2 = 8 + -8

Combine like terms: 8 + -8 = 0
26x + 21x2 = 0

Solving
26x + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(26 + 21x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(26 + 21x)' equal to zero and attempt to solve:

Simplifying
26 + 21x = 0

Solving
26 + 21x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-26' to each side of the equation.
26 + -26 + 21x = 0 + -26

Combine like terms: 26 + -26 = 0
0 + 21x = 0 + -26
21x = 0 + -26

Combine like terms: 0 + -26 = -26
21x = -26

Divide each side by '21'.
x = -1.238095238

Simplifying
x = -1.238095238
Solution
x = {0, -1.238095238}

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