(2x+6)(4x+7)=0

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Solution for (2x+6)(4x+7)=0 equation: 


Simplifying
(2x + 6)(4x + 7) = 0

Reorder the terms:
(6 + 2x)(4x + 7) = 0

Reorder the terms:
(6 + 2x)(7 + 4x) = 0

Multiply (6 + 2x) * (7 + 4x)
(6(7 + 4x) + 2x * (7 + 4x)) = 0
((7 * 6 + 4x * 6) + 2x * (7 + 4x)) = 0
((42 + 24x) + 2x * (7 + 4x)) = 0
(42 + 24x + (7 * 2x + 4x * 2x)) = 0
(42 + 24x + (14x + 8x2)) = 0

Combine like terms: 24x + 14x = 38x
(42 + 38x + 8x2) = 0

Solving
42 + 38x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + 19x + 4x2) = 0

Factor a trinomial.
2((3 + x)(7 + 4x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(7 + 4x)' equal to zero and attempt to solve:

Simplifying
7 + 4x = 0

Solving
7 + 4x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4x = 0 + -7
4x = 0 + -7

Combine like terms: 0 + -7 = -7
4x = -7

Divide each side by '4'.
x = -1.75

Simplifying
x = -1.75
Solution
x = {-3, -1.75}

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