5x^2+6x=33x-10

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Solution for 5x^2+6x=33x-10 equation: 


Simplifying
5x2 + 6x = 33x + -10

Reorder the terms:
6x + 5x2 = 33x + -10

Reorder the terms:
6x + 5x2 = -10 + 33x

Solving
6x + 5x2 = -10 + 33x

Solving for variable 'x'.

Reorder the terms:
10 + 6x + -33x + 5x2 = -10 + 33x + 10 + -33x

Combine like terms: 6x + -33x = -27x
10 + -27x + 5x2 = -10 + 33x + 10 + -33x

Reorder the terms:
10 + -27x + 5x2 = -10 + 10 + 33x + -33x

Combine like terms: -10 + 10 = 0
10 + -27x + 5x2 = 0 + 33x + -33x
10 + -27x + 5x2 = 33x + -33x

Combine like terms: 33x + -33x = 0
10 + -27x + 5x2 = 0

Factor a trinomial.
(2 + -5x)(5 + -1x) = 0


Subproblem 1
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 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 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0.4, 5}

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