9x^2-4-(3x-2)(x+5)=0

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Solution for 9x^2-4-(3x-2)(x+5)=0 equation:


Simplifying
9x2 + -4 + -1(3x + -2)(x + 5) = 0

Reorder the terms:
9x2 + -4 + -1(-2 + 3x)(x + 5) = 0

Reorder the terms:
9x2 + -4 + -1(-2 + 3x)(5 + x) = 0

Multiply (-2 + 3x) * (5 + x)
9x2 + -4 + -1(-2(5 + x) + 3x * (5 + x)) = 0
9x2 + -4 + -1((5 * -2 + x * -2) + 3x * (5 + x)) = 0
9x2 + -4 + -1((-10 + -2x) + 3x * (5 + x)) = 0
9x2 + -4 + -1(-10 + -2x + (5 * 3x + x * 3x)) = 0
9x2 + -4 + -1(-10 + -2x + (15x + 3x2)) = 0

Combine like terms: -2x + 15x = 13x
9x2 + -4 + -1(-10 + 13x + 3x2) = 0
9x2 + -4 + (-10 * -1 + 13x * -1 + 3x2 * -1) = 0
9x2 + -4 + (10 + -13x + -3x2) = 0

Reorder the terms:
-4 + 10 + -13x + 9x2 + -3x2 = 0

Combine like terms: -4 + 10 = 6
6 + -13x + 9x2 + -3x2 = 0

Combine like terms: 9x2 + -3x2 = 6x2
6 + -13x + 6x2 = 0

Solving
6 + -13x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -3x)(3 + -2x) = 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 '(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 = {0.6666666667, 1.5}

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