(x+2)(3x-5)=(9x^2-25)

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Solution for (x+2)(3x-5)=(9x^2-25) equation: 


Simplifying
(x + 2)(3x + -5) = (9x2 + -25)

Reorder the terms:
(2 + x)(3x + -5) = (9x2 + -25)

Reorder the terms:
(2 + x)(-5 + 3x) = (9x2 + -25)

Multiply (2 + x) * (-5 + 3x)
(2(-5 + 3x) + x(-5 + 3x)) = (9x2 + -25)
((-5 * 2 + 3x * 2) + x(-5 + 3x)) = (9x2 + -25)
((-10 + 6x) + x(-5 + 3x)) = (9x2 + -25)
(-10 + 6x + (-5 * x + 3x * x)) = (9x2 + -25)
(-10 + 6x + (-5x + 3x2)) = (9x2 + -25)

Combine like terms: 6x + -5x = 1x
(-10 + 1x + 3x2) = (9x2 + -25)

Reorder the terms:
-10 + 1x + 3x2 = (-25 + 9x2)

Remove parenthesis around (-25 + 9x2)
-10 + 1x + 3x2 = -25 + 9x2

Solving
-10 + 1x + 3x2 = -25 + 9x2

Solving for variable 'x'.

Reorder the terms:
-10 + 25 + 1x + 3x2 + -9x2 = -25 + 9x2 + 25 + -9x2

Combine like terms: -10 + 25 = 15
15 + 1x + 3x2 + -9x2 = -25 + 9x2 + 25 + -9x2

Combine like terms: 3x2 + -9x2 = -6x2
15 + 1x + -6x2 = -25 + 9x2 + 25 + -9x2

Reorder the terms:
15 + 1x + -6x2 = -25 + 25 + 9x2 + -9x2

Combine like terms: -25 + 25 = 0
15 + 1x + -6x2 = 0 + 9x2 + -9x2
15 + 1x + -6x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
15 + 1x + -6x2 = 0

Factor a trinomial.
(5 + -3x)(3 + 2x) = 0


Subproblem 1
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667

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 = {1.666666667, -1.5}

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