4x^2-9=(8x-12)(x-3)

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Solution for 4x^2-9=(8x-12)(x-3) equation: 


Simplifying
4x2 + -9 = (8x + -12)(x + -3)

Reorder the terms:
-9 + 4x2 = (8x + -12)(x + -3)

Reorder the terms:
-9 + 4x2 = (-12 + 8x)(x + -3)

Reorder the terms:
-9 + 4x2 = (-12 + 8x)(-3 + x)

Multiply (-12 + 8x) * (-3 + x)
-9 + 4x2 = (-12(-3 + x) + 8x * (-3 + x))
-9 + 4x2 = ((-3 * -12 + x * -12) + 8x * (-3 + x))
-9 + 4x2 = ((36 + -12x) + 8x * (-3 + x))
-9 + 4x2 = (36 + -12x + (-3 * 8x + x * 8x))
-9 + 4x2 = (36 + -12x + (-24x + 8x2))

Combine like terms: -12x + -24x = -36x
-9 + 4x2 = (36 + -36x + 8x2)

Solving
-9 + 4x2 = 36 + -36x + 8x2

Solving for variable 'x'.

Reorder the terms:
-9 + -36 + 36x + 4x2 + -8x2 = 36 + -36x + 8x2 + -36 + 36x + -8x2

Combine like terms: -9 + -36 = -45
-45 + 36x + 4x2 + -8x2 = 36 + -36x + 8x2 + -36 + 36x + -8x2

Combine like terms: 4x2 + -8x2 = -4x2
-45 + 36x + -4x2 = 36 + -36x + 8x2 + -36 + 36x + -8x2

Reorder the terms:
-45 + 36x + -4x2 = 36 + -36 + -36x + 36x + 8x2 + -8x2

Combine like terms: 36 + -36 = 0
-45 + 36x + -4x2 = 0 + -36x + 36x + 8x2 + -8x2
-45 + 36x + -4x2 = -36x + 36x + 8x2 + -8x2

Combine like terms: -36x + 36x = 0
-45 + 36x + -4x2 = 0 + 8x2 + -8x2
-45 + 36x + -4x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-45 + 36x + -4x2 = 0

Factor a trinomial.
(-15 + 2x)(3 + -2x) = 0


Subproblem 1
Set the factor '(-15 + 2x)' equal to zero and attempt to solve:

Simplifying
-15 + 2x = 0

Solving
-15 + 2x = 0

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

Add '15' to each side of the equation.
-15 + 15 + 2x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 2x = 0 + 15
2x = 0 + 15

Combine like terms: 0 + 15 = 15
2x = 15

Divide each side by '2'.
x = 7.5

Simplifying
x = 7.5

Subproblem 2
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
Solution
x = {7.5, 1.5}

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