9x^2-12x+4=(7x+15)(9x-6)

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Solution for 9x^2-12x+4=(7x+15)(9x-6) equation: 


Simplifying
9x2 + -12x + 4 = (7x + 15)(9x + -6)

Reorder the terms:
4 + -12x + 9x2 = (7x + 15)(9x + -6)

Reorder the terms:
4 + -12x + 9x2 = (15 + 7x)(9x + -6)

Reorder the terms:
4 + -12x + 9x2 = (15 + 7x)(-6 + 9x)

Multiply (15 + 7x) * (-6 + 9x)
4 + -12x + 9x2 = (15(-6 + 9x) + 7x * (-6 + 9x))
4 + -12x + 9x2 = ((-6 * 15 + 9x * 15) + 7x * (-6 + 9x))
4 + -12x + 9x2 = ((-90 + 135x) + 7x * (-6 + 9x))
4 + -12x + 9x2 = (-90 + 135x + (-6 * 7x + 9x * 7x))
4 + -12x + 9x2 = (-90 + 135x + (-42x + 63x2))

Combine like terms: 135x + -42x = 93x
4 + -12x + 9x2 = (-90 + 93x + 63x2)

Solving
4 + -12x + 9x2 = -90 + 93x + 63x2

Solving for variable 'x'.

Reorder the terms:
4 + 90 + -12x + -93x + 9x2 + -63x2 = -90 + 93x + 63x2 + 90 + -93x + -63x2

Combine like terms: 4 + 90 = 94
94 + -12x + -93x + 9x2 + -63x2 = -90 + 93x + 63x2 + 90 + -93x + -63x2

Combine like terms: -12x + -93x = -105x
94 + -105x + 9x2 + -63x2 = -90 + 93x + 63x2 + 90 + -93x + -63x2

Combine like terms: 9x2 + -63x2 = -54x2
94 + -105x + -54x2 = -90 + 93x + 63x2 + 90 + -93x + -63x2

Reorder the terms:
94 + -105x + -54x2 = -90 + 90 + 93x + -93x + 63x2 + -63x2

Combine like terms: -90 + 90 = 0
94 + -105x + -54x2 = 0 + 93x + -93x + 63x2 + -63x2
94 + -105x + -54x2 = 93x + -93x + 63x2 + -63x2

Combine like terms: 93x + -93x = 0
94 + -105x + -54x2 = 0 + 63x2 + -63x2
94 + -105x + -54x2 = 63x2 + -63x2

Combine like terms: 63x2 + -63x2 = 0
94 + -105x + -54x2 = 0

Factor a trinomial.
(2 + -3x)(47 + 18x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(47 + 18x)' equal to zero and attempt to solve:

Simplifying
47 + 18x = 0

Solving
47 + 18x = 0

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

Add '-47' to each side of the equation.
47 + -47 + 18x = 0 + -47

Combine like terms: 47 + -47 = 0
0 + 18x = 0 + -47
18x = 0 + -47

Combine like terms: 0 + -47 = -47
18x = -47

Divide each side by '18'.
x = -2.611111111

Simplifying
x = -2.611111111
Solution
x = {0.6666666667, -2.611111111}

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