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

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


Simplifying
4x2 + -9 = (2x + 3)(3x + -5)

Reorder the terms:
-9 + 4x2 = (2x + 3)(3x + -5)

Reorder the terms:
-9 + 4x2 = (3 + 2x)(3x + -5)

Reorder the terms:
-9 + 4x2 = (3 + 2x)(-5 + 3x)

Multiply (3 + 2x) * (-5 + 3x)
-9 + 4x2 = (3(-5 + 3x) + 2x * (-5 + 3x))
-9 + 4x2 = ((-5 * 3 + 3x * 3) + 2x * (-5 + 3x))
-9 + 4x2 = ((-15 + 9x) + 2x * (-5 + 3x))
-9 + 4x2 = (-15 + 9x + (-5 * 2x + 3x * 2x))
-9 + 4x2 = (-15 + 9x + (-10x + 6x2))

Combine like terms: 9x + -10x = -1x
-9 + 4x2 = (-15 + -1x + 6x2)

Solving
-9 + 4x2 = -15 + -1x + 6x2

Solving for variable 'x'.

Reorder the terms:
-9 + 15 + x + 4x2 + -6x2 = -15 + -1x + 6x2 + 15 + x + -6x2

Combine like terms: -9 + 15 = 6
6 + x + 4x2 + -6x2 = -15 + -1x + 6x2 + 15 + x + -6x2

Combine like terms: 4x2 + -6x2 = -2x2
6 + x + -2x2 = -15 + -1x + 6x2 + 15 + x + -6x2

Reorder the terms:
6 + x + -2x2 = -15 + 15 + -1x + x + 6x2 + -6x2

Combine like terms: -15 + 15 = 0
6 + x + -2x2 = 0 + -1x + x + 6x2 + -6x2
6 + x + -2x2 = -1x + x + 6x2 + -6x2

Combine like terms: -1x + x = 0
6 + x + -2x2 = 0 + 6x2 + -6x2
6 + x + -2x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
6 + x + -2x2 = 0

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


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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 = {2, -1.5}

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