6x^2-8x+29=4+22x-3x^2

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Solution for 6x^2-8x+29=4+22x-3x^2 equation: 


Simplifying
6x2 + -8x + 29 = 4 + 22x + -3x2

Reorder the terms:
29 + -8x + 6x2 = 4 + 22x + -3x2

Solving
29 + -8x + 6x2 = 4 + 22x + -3x2

Solving for variable 'x'.

Reorder the terms:
29 + -4 + -8x + -22x + 6x2 + 3x2 = 4 + 22x + -3x2 + -4 + -22x + 3x2

Combine like terms: 29 + -4 = 25
25 + -8x + -22x + 6x2 + 3x2 = 4 + 22x + -3x2 + -4 + -22x + 3x2

Combine like terms: -8x + -22x = -30x
25 + -30x + 6x2 + 3x2 = 4 + 22x + -3x2 + -4 + -22x + 3x2

Combine like terms: 6x2 + 3x2 = 9x2
25 + -30x + 9x2 = 4 + 22x + -3x2 + -4 + -22x + 3x2

Reorder the terms:
25 + -30x + 9x2 = 4 + -4 + 22x + -22x + -3x2 + 3x2

Combine like terms: 4 + -4 = 0
25 + -30x + 9x2 = 0 + 22x + -22x + -3x2 + 3x2
25 + -30x + 9x2 = 22x + -22x + -3x2 + 3x2

Combine like terms: 22x + -22x = 0
25 + -30x + 9x2 = 0 + -3x2 + 3x2
25 + -30x + 9x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
25 + -30x + 9x2 = 0

Factor a trinomial.
(5 + -3x)(5 + -3x) = 0


Subproblem 1
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {1.666666667, 1.666666667}

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