(x-7x+4)(2x-3x-6)=0

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Solution for (x-7x+4)(2x-3x-6)=0 equation: 


Simplifying
(x + -7x + 4)(2x + -3x + -6) = 0

Reorder the terms:
(4 + x + -7x)(2x + -3x + -6) = 0

Combine like terms: x + -7x = -6x
(4 + -6x)(2x + -3x + -6) = 0

Reorder the terms:
(4 + -6x)(-6 + 2x + -3x) = 0

Combine like terms: 2x + -3x = -1x
(4 + -6x)(-6 + -1x) = 0

Multiply (4 + -6x) * (-6 + -1x)
(4(-6 + -1x) + -6x * (-6 + -1x)) = 0
((-6 * 4 + -1x * 4) + -6x * (-6 + -1x)) = 0
((-24 + -4x) + -6x * (-6 + -1x)) = 0
(-24 + -4x + (-6 * -6x + -1x * -6x)) = 0
(-24 + -4x + (36x + 6x2)) = 0

Combine like terms: -4x + 36x = 32x
(-24 + 32x + 6x2) = 0

Solving
-24 + 32x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 16x + 3x2) = 0

Factor a trinomial.
2((-6 + -1x)(2 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

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

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

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
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
Solution
x = {-6, 0.6666666667}

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