x(9x+5)=4x^2-3x+21

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Solution for x(9x+5)=4x^2-3x+21 equation: 


Simplifying
x(9x + 5) = 4x2 + -3x + 21

Reorder the terms:
x(5 + 9x) = 4x2 + -3x + 21
(5 * x + 9x * x) = 4x2 + -3x + 21
(5x + 9x2) = 4x2 + -3x + 21

Reorder the terms:
5x + 9x2 = 21 + -3x + 4x2

Solving
5x + 9x2 = 21 + -3x + 4x2

Solving for variable 'x'.

Reorder the terms:
-21 + 5x + 3x + 9x2 + -4x2 = 21 + -3x + 4x2 + -21 + 3x + -4x2

Combine like terms: 5x + 3x = 8x
-21 + 8x + 9x2 + -4x2 = 21 + -3x + 4x2 + -21 + 3x + -4x2

Combine like terms: 9x2 + -4x2 = 5x2
-21 + 8x + 5x2 = 21 + -3x + 4x2 + -21 + 3x + -4x2

Reorder the terms:
-21 + 8x + 5x2 = 21 + -21 + -3x + 3x + 4x2 + -4x2

Combine like terms: 21 + -21 = 0
-21 + 8x + 5x2 = 0 + -3x + 3x + 4x2 + -4x2
-21 + 8x + 5x2 = -3x + 3x + 4x2 + -4x2

Combine like terms: -3x + 3x = 0
-21 + 8x + 5x2 = 0 + 4x2 + -4x2
-21 + 8x + 5x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-21 + 8x + 5x2 = 0

Factor a trinomial.
(-3 + -1x)(7 + -5x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(7 + -5x)' equal to zero and attempt to solve:

Simplifying
7 + -5x = 0

Solving
7 + -5x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5x = 0 + -7
-5x = 0 + -7

Combine like terms: 0 + -7 = -7
-5x = -7

Divide each side by '-5'.
x = 1.4

Simplifying
x = 1.4
Solution
x = {-3, 1.4}

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