6x^2+4=10x+48

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Solution for 6x^2+4=10x+48 equation: 


Simplifying
6x2 + 4 = 10x + 48

Reorder the terms:
4 + 6x2 = 10x + 48

Reorder the terms:
4 + 6x2 = 48 + 10x

Solving
4 + 6x2 = 48 + 10x

Solving for variable 'x'.

Reorder the terms:
4 + -48 + -10x + 6x2 = 48 + 10x + -48 + -10x

Combine like terms: 4 + -48 = -44
-44 + -10x + 6x2 = 48 + 10x + -48 + -10x

Reorder the terms:
-44 + -10x + 6x2 = 48 + -48 + 10x + -10x

Combine like terms: 48 + -48 = 0
-44 + -10x + 6x2 = 0 + 10x + -10x
-44 + -10x + 6x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-44 + -10x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-22 + -5x + 3x2) = 0

Factor a trinomial.
2((-2 + -1x)(11 + -3x)) = 0

Ignore the factor 2.

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 '(11 + -3x)' equal to zero and attempt to solve:

Simplifying
11 + -3x = 0

Solving
11 + -3x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -3x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3x = 0 + -11
-3x = 0 + -11

Combine like terms: 0 + -11 = -11
-3x = -11

Divide each side by '-3'.
x = 3.666666667

Simplifying
x = 3.666666667
Solution
x = {-2, 3.666666667}

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