3x^2-29x=-2x^2-5x-16

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Solution for 3x^2-29x=-2x^2-5x-16 equation: 


Simplifying
3x2 + -29x = -2x2 + -5x + -16

Reorder the terms:
-29x + 3x2 = -2x2 + -5x + -16

Reorder the terms:
-29x + 3x2 = -16 + -5x + -2x2

Solving
-29x + 3x2 = -16 + -5x + -2x2

Solving for variable 'x'.

Reorder the terms:
16 + -29x + 5x + 3x2 + 2x2 = -16 + -5x + -2x2 + 16 + 5x + 2x2

Combine like terms: -29x + 5x = -24x
16 + -24x + 3x2 + 2x2 = -16 + -5x + -2x2 + 16 + 5x + 2x2

Combine like terms: 3x2 + 2x2 = 5x2
16 + -24x + 5x2 = -16 + -5x + -2x2 + 16 + 5x + 2x2

Reorder the terms:
16 + -24x + 5x2 = -16 + 16 + -5x + 5x + -2x2 + 2x2

Combine like terms: -16 + 16 = 0
16 + -24x + 5x2 = 0 + -5x + 5x + -2x2 + 2x2
16 + -24x + 5x2 = -5x + 5x + -2x2 + 2x2

Combine like terms: -5x + 5x = 0
16 + -24x + 5x2 = 0 + -2x2 + 2x2
16 + -24x + 5x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
16 + -24x + 5x2 = 0

Factor a trinomial.
(4 + -5x)(4 + -1x) = 0


Subproblem 1
Set the factor '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

Solving
4 + -5x = 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 + -5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x = 0 + -4
-5x = 0 + -4

Combine like terms: 0 + -4 = -4
-5x = -4

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8

Subproblem 2
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
Solution
x = {0.8, 4}

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