x^2+7x=2x+3x*2x^2

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Solution for x^2+7x=2x+3x*2x^2 equation:


Simplifying
x2 + 7x = 2x + 3x * 2x2

Reorder the terms:
7x + x2 = 2x + 3x * 2x2

Reorder the terms for easier multiplication:
7x + x2 = 2x + 3 * 2x * x2

Multiply 3 * 2
7x + x2 = 2x + 6x * x2

Multiply x * x2
7x + x2 = 2x + 6x3

Solving
7x + x2 = 2x + 6x3

Solving for variable 'x'.

Reorder the terms:
7x + -2x + x2 + -6x3 = 2x + 6x3 + -2x + -6x3

Combine like terms: 7x + -2x = 5x
5x + x2 + -6x3 = 2x + 6x3 + -2x + -6x3

Reorder the terms:
5x + x2 + -6x3 = 2x + -2x + 6x3 + -6x3

Combine like terms: 2x + -2x = 0
5x + x2 + -6x3 = 0 + 6x3 + -6x3
5x + x2 + -6x3 = 6x3 + -6x3

Combine like terms: 6x3 + -6x3 = 0
5x + x2 + -6x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + x + -6x2) = 0

Factor a trinomial.
x((1 + -1x)(5 + 6x)) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
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 3
Set the factor '(5 + 6x)' equal to zero and attempt to solve:

Simplifying
5 + 6x = 0

Solving
5 + 6x = 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 + 6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6x = 0 + -5
6x = 0 + -5

Combine like terms: 0 + -5 = -5
6x = -5

Divide each side by '6'.
x = -0.8333333333

Simplifying
x = -0.8333333333
Solution
x = {0, 1, -0.8333333333}

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