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

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


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

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

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

Multiply (-3 + x) * (3 + 2x)
4x2 + (-3(3 + 2x) + x(3 + 2x)) = 0
4x2 + ((3 * -3 + 2x * -3) + x(3 + 2x)) = 0
4x2 + ((-9 + -6x) + x(3 + 2x)) = 0
4x2 + (-9 + -6x + (3 * x + 2x * x)) = 0
4x2 + (-9 + -6x + (3x + 2x2)) = 0

Combine like terms: -6x + 3x = -3x
4x2 + (-9 + -3x + 2x2) = 0

Reorder the terms:
-9 + -3x + 4x2 + 2x2 = 0

Combine like terms: 4x2 + 2x2 = 6x2
-9 + -3x + 6x2 = 0

Solving
-9 + -3x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -1x + 2x2) = 0

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

Ignore the factor 3.

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1x = 0 + 1

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

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

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

Simplifying
x = -1

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, 1.5}

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