6x^2+16=x(x+42)

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Solution for 6x^2+16=x(x+42) equation: 


Simplifying
6x2 + 16 = x(x + 42)

Reorder the terms:
16 + 6x2 = x(x + 42)

Reorder the terms:
16 + 6x2 = x(42 + x)
16 + 6x2 = (42 * x + x * x)
16 + 6x2 = (42x + x2)

Solving
16 + 6x2 = 42x + x2

Solving for variable 'x'.

Reorder the terms:
16 + -42x + 6x2 + -1x2 = 42x + x2 + -42x + -1x2

Combine like terms: 6x2 + -1x2 = 5x2
16 + -42x + 5x2 = 42x + x2 + -42x + -1x2

Reorder the terms:
16 + -42x + 5x2 = 42x + -42x + x2 + -1x2

Combine like terms: 42x + -42x = 0
16 + -42x + 5x2 = 0 + x2 + -1x2
16 + -42x + 5x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
16 + -42x + 5x2 = 0

Factor a trinomial.
(2 + -5x)(8 + -1x) = 0


Subproblem 1
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 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 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {0.4, 8}

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