x(5x+1)=2x^2-3x+4

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Solution for x(5x+1)=2x^2-3x+4 equation: 


Simplifying
x(5x + 1) = 2x2 + -3x + 4

Reorder the terms:
x(1 + 5x) = 2x2 + -3x + 4
(1 * x + 5x * x) = 2x2 + -3x + 4
(1x + 5x2) = 2x2 + -3x + 4

Reorder the terms:
1x + 5x2 = 4 + -3x + 2x2

Solving
1x + 5x2 = 4 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
-4 + 1x + 3x + 5x2 + -2x2 = 4 + -3x + 2x2 + -4 + 3x + -2x2

Combine like terms: 1x + 3x = 4x
-4 + 4x + 5x2 + -2x2 = 4 + -3x + 2x2 + -4 + 3x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-4 + 4x + 3x2 = 4 + -3x + 2x2 + -4 + 3x + -2x2

Reorder the terms:
-4 + 4x + 3x2 = 4 + -4 + -3x + 3x + 2x2 + -2x2

Combine like terms: 4 + -4 = 0
-4 + 4x + 3x2 = 0 + -3x + 3x + 2x2 + -2x2
-4 + 4x + 3x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
-4 + 4x + 3x2 = 0 + 2x2 + -2x2
-4 + 4x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4 + 4x + 3x2 = 0

Factor a trinomial.
(-2 + -1x)(2 + -3x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-2, 0.6666666667}

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