x(9x+1)=4x^2-7x+4

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Solution for x(9x+1)=4x^2-7x+4 equation: 


Simplifying
x(9x + 1) = 4x2 + -7x + 4

Reorder the terms:
x(1 + 9x) = 4x2 + -7x + 4
(1 * x + 9x * x) = 4x2 + -7x + 4
(1x + 9x2) = 4x2 + -7x + 4

Reorder the terms:
1x + 9x2 = 4 + -7x + 4x2

Solving
1x + 9x2 = 4 + -7x + 4x2

Solving for variable 'x'.

Reorder the terms:
-4 + 1x + 7x + 9x2 + -4x2 = 4 + -7x + 4x2 + -4 + 7x + -4x2

Combine like terms: 1x + 7x = 8x
-4 + 8x + 9x2 + -4x2 = 4 + -7x + 4x2 + -4 + 7x + -4x2

Combine like terms: 9x2 + -4x2 = 5x2
-4 + 8x + 5x2 = 4 + -7x + 4x2 + -4 + 7x + -4x2

Reorder the terms:
-4 + 8x + 5x2 = 4 + -4 + -7x + 7x + 4x2 + -4x2

Combine like terms: 4 + -4 = 0
-4 + 8x + 5x2 = 0 + -7x + 7x + 4x2 + -4x2
-4 + 8x + 5x2 = -7x + 7x + 4x2 + -4x2

Combine like terms: -7x + 7x = 0
-4 + 8x + 5x2 = 0 + 4x2 + -4x2
-4 + 8x + 5x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-4 + 8x + 5x2 = 0

Factor a trinomial.
(-2 + -1x)(2 + -5x) = 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 + -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
Solution
x = {-2, 0.4}

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