4x^2+6x-38=2x+10

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Solution for 4x^2+6x-38=2x+10 equation: 


Simplifying
4x2 + 6x + -38 = 2x + 10

Reorder the terms:
-38 + 6x + 4x2 = 2x + 10

Reorder the terms:
-38 + 6x + 4x2 = 10 + 2x

Solving
-38 + 6x + 4x2 = 10 + 2x

Solving for variable 'x'.

Reorder the terms:
-38 + -10 + 6x + -2x + 4x2 = 10 + 2x + -10 + -2x

Combine like terms: -38 + -10 = -48
-48 + 6x + -2x + 4x2 = 10 + 2x + -10 + -2x

Combine like terms: 6x + -2x = 4x
-48 + 4x + 4x2 = 10 + 2x + -10 + -2x

Reorder the terms:
-48 + 4x + 4x2 = 10 + -10 + 2x + -2x

Combine like terms: 10 + -10 = 0
-48 + 4x + 4x2 = 0 + 2x + -2x
-48 + 4x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-48 + 4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + x + x2) = 0

Factor a trinomial.
4((-4 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-4, 3}

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