(9x-6)(4x+7)=0

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Solution for (9x-6)(4x+7)=0 equation: 


Simplifying
(9x + -6)(4x + 7) = 0

Reorder the terms:
(-6 + 9x)(4x + 7) = 0

Reorder the terms:
(-6 + 9x)(7 + 4x) = 0

Multiply (-6 + 9x) * (7 + 4x)
(-6(7 + 4x) + 9x * (7 + 4x)) = 0
((7 * -6 + 4x * -6) + 9x * (7 + 4x)) = 0
((-42 + -24x) + 9x * (7 + 4x)) = 0
(-42 + -24x + (7 * 9x + 4x * 9x)) = 0
(-42 + -24x + (63x + 36x2)) = 0

Combine like terms: -24x + 63x = 39x
(-42 + 39x + 36x2) = 0

Solving
-42 + 39x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 13x + 12x2) = 0

Factor a trinomial.
3((-7 + -4x)(2 + -3x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + -4x)' equal to zero and attempt to solve:

Simplifying
-7 + -4x = 0

Solving
-7 + -4x = 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 + -4x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -4x = 0 + 7
-4x = 0 + 7

Combine like terms: 0 + 7 = 7
-4x = 7

Divide each side by '-4'.
x = -1.75

Simplifying
x = -1.75

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 = {-1.75, 0.6666666667}

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