x(6x-5)=4x^2+4x-9

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Solution for x(6x-5)=4x^2+4x-9 equation: 


Simplifying
x(6x + -5) = 4x2 + 4x + -9

Reorder the terms:
x(-5 + 6x) = 4x2 + 4x + -9
(-5 * x + 6x * x) = 4x2 + 4x + -9
(-5x + 6x2) = 4x2 + 4x + -9

Reorder the terms:
-5x + 6x2 = -9 + 4x + 4x2

Solving
-5x + 6x2 = -9 + 4x + 4x2

Solving for variable 'x'.

Reorder the terms:
9 + -5x + -4x + 6x2 + -4x2 = -9 + 4x + 4x2 + 9 + -4x + -4x2

Combine like terms: -5x + -4x = -9x
9 + -9x + 6x2 + -4x2 = -9 + 4x + 4x2 + 9 + -4x + -4x2

Combine like terms: 6x2 + -4x2 = 2x2
9 + -9x + 2x2 = -9 + 4x + 4x2 + 9 + -4x + -4x2

Reorder the terms:
9 + -9x + 2x2 = -9 + 9 + 4x + -4x + 4x2 + -4x2

Combine like terms: -9 + 9 = 0
9 + -9x + 2x2 = 0 + 4x + -4x + 4x2 + -4x2
9 + -9x + 2x2 = 4x + -4x + 4x2 + -4x2

Combine like terms: 4x + -4x = 0
9 + -9x + 2x2 = 0 + 4x2 + -4x2
9 + -9x + 2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
9 + -9x + 2x2 = 0

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


Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

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

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

Subproblem 2
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
Solution
x = {1.5, 3}

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