(x+2)(x+4)=6x^2

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


Simplifying
(x + 2)(x + 4) = 6x2

Reorder the terms:
(2 + x)(x + 4) = 6x2

Reorder the terms:
(2 + x)(4 + x) = 6x2

Multiply (2 + x) * (4 + x)
(2(4 + x) + x(4 + x)) = 6x2
((4 * 2 + x * 2) + x(4 + x)) = 6x2
((8 + 2x) + x(4 + x)) = 6x2
(8 + 2x + (4 * x + x * x)) = 6x2
(8 + 2x + (4x + x2)) = 6x2

Combine like terms: 2x + 4x = 6x
(8 + 6x + x2) = 6x2

Solving
8 + 6x + x2 = 6x2

Solving for variable 'x'.

Combine like terms: x2 + -6x2 = -5x2
8 + 6x + -5x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
8 + 6x + -5x2 = 0

Factor a trinomial.
(2 + -1x)(4 + 5x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4 + 5x)' equal to zero and attempt to solve:

Simplifying
4 + 5x = 0

Solving
4 + 5x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5x = 0 + -4
5x = 0 + -4

Combine like terms: 0 + -4 = -4
5x = -4

Divide each side by '5'.
x = -0.8

Simplifying
x = -0.8
Solution
x = {2, -0.8}

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