4x^2-12x+9=(4x-6)(3x+5)

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Solution for 4x^2-12x+9=(4x-6)(3x+5) equation: 


Simplifying
4x2 + -12x + 9 = (4x + -6)(3x + 5)

Reorder the terms:
9 + -12x + 4x2 = (4x + -6)(3x + 5)

Reorder the terms:
9 + -12x + 4x2 = (-6 + 4x)(3x + 5)

Reorder the terms:
9 + -12x + 4x2 = (-6 + 4x)(5 + 3x)

Multiply (-6 + 4x) * (5 + 3x)
9 + -12x + 4x2 = (-6(5 + 3x) + 4x * (5 + 3x))
9 + -12x + 4x2 = ((5 * -6 + 3x * -6) + 4x * (5 + 3x))
9 + -12x + 4x2 = ((-30 + -18x) + 4x * (5 + 3x))
9 + -12x + 4x2 = (-30 + -18x + (5 * 4x + 3x * 4x))
9 + -12x + 4x2 = (-30 + -18x + (20x + 12x2))

Combine like terms: -18x + 20x = 2x
9 + -12x + 4x2 = (-30 + 2x + 12x2)

Solving
9 + -12x + 4x2 = -30 + 2x + 12x2

Solving for variable 'x'.

Reorder the terms:
9 + 30 + -12x + -2x + 4x2 + -12x2 = -30 + 2x + 12x2 + 30 + -2x + -12x2

Combine like terms: 9 + 30 = 39
39 + -12x + -2x + 4x2 + -12x2 = -30 + 2x + 12x2 + 30 + -2x + -12x2

Combine like terms: -12x + -2x = -14x
39 + -14x + 4x2 + -12x2 = -30 + 2x + 12x2 + 30 + -2x + -12x2

Combine like terms: 4x2 + -12x2 = -8x2
39 + -14x + -8x2 = -30 + 2x + 12x2 + 30 + -2x + -12x2

Reorder the terms:
39 + -14x + -8x2 = -30 + 30 + 2x + -2x + 12x2 + -12x2

Combine like terms: -30 + 30 = 0
39 + -14x + -8x2 = 0 + 2x + -2x + 12x2 + -12x2
39 + -14x + -8x2 = 2x + -2x + 12x2 + -12x2

Combine like terms: 2x + -2x = 0
39 + -14x + -8x2 = 0 + 12x2 + -12x2
39 + -14x + -8x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
39 + -14x + -8x2 = 0

Factor a trinomial.
(3 + -2x)(13 + 4x) = 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 '(13 + 4x)' equal to zero and attempt to solve:

Simplifying
13 + 4x = 0

Solving
13 + 4x = 0

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

Add '-13' to each side of the equation.
13 + -13 + 4x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 4x = 0 + -13
4x = 0 + -13

Combine like terms: 0 + -13 = -13
4x = -13

Divide each side by '4'.
x = -3.25

Simplifying
x = -3.25
Solution
x = {1.5, -3.25}

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