2((-7+-3x)(3+-2x))=0

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Solution for 2((-7+-3x)(3+-2x))=0 equation: 


Simplifying
2((-7 + -3x)(3 + -2x)) = 0

Multiply (-7 + -3x) * (3 + -2x)
2((-7(3 + -2x) + -3x * (3 + -2x))) = 0
2(((3 * -7 + -2x * -7) + -3x * (3 + -2x))) = 0
2(((-21 + 14x) + -3x * (3 + -2x))) = 0
2((-21 + 14x + (3 * -3x + -2x * -3x))) = 0
2((-21 + 14x + (-9x + 6x2))) = 0

Combine like terms: 14x + -9x = 5x
2((-21 + 5x + 6x2)) = 0
(-21 * 2 + 5x * 2 + 6x2 * 2) = 0
(-42 + 10x + 12x2) = 0

Solving
-42 + 10x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 5x + 6x2) = 0

Factor a trinomial.
2((-7 + -3x)(3 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -3x)' equal to zero and attempt to solve:

Simplifying
-7 + -3x = 0

Solving
-7 + -3x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3x = 0 + 7
-3x = 0 + 7

Combine like terms: 0 + 7 = 7
-3x = 7

Divide each side by '-3'.
x = -2.333333333

Simplifying
x = -2.333333333

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 = {-2.333333333, 1.5}

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