3x^2-7x+29=x^2+4x+4x+16

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Solution for 3x^2-7x+29=x^2+4x+4x+16 equation: 


Simplifying
3x2 + -7x + 29 = x2 + 4x + 4x + 16

Reorder the terms:
29 + -7x + 3x2 = x2 + 4x + 4x + 16

Reorder the terms:
29 + -7x + 3x2 = 16 + 4x + 4x + x2

Combine like terms: 4x + 4x = 8x
29 + -7x + 3x2 = 16 + 8x + x2

Solving
29 + -7x + 3x2 = 16 + 8x + x2

Solving for variable 'x'.

Reorder the terms:
29 + -16 + -7x + -8x + 3x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Combine like terms: 29 + -16 = 13
13 + -7x + -8x + 3x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Combine like terms: -7x + -8x = -15x
13 + -15x + 3x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
13 + -15x + 2x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Reorder the terms:
13 + -15x + 2x2 = 16 + -16 + 8x + -8x + x2 + -1x2

Combine like terms: 16 + -16 = 0
13 + -15x + 2x2 = 0 + 8x + -8x + x2 + -1x2
13 + -15x + 2x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
13 + -15x + 2x2 = 0 + x2 + -1x2
13 + -15x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
13 + -15x + 2x2 = 0

Factor a trinomial.
(1 + -1x)(13 + -2x) = 0


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(13 + -2x)' equal to zero and attempt to solve:

Simplifying
13 + -2x = 0

Solving
13 + -2x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -2x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2x = 0 + -13
-2x = 0 + -13

Combine like terms: 0 + -13 = -13
-2x = -13

Divide each side by '-2'.
x = 6.5

Simplifying
x = 6.5
Solution
x = {1, 6.5}

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