(7x-9)(6x+8)=0

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Solution for (7x-9)(6x+8)=0 equation: 


Simplifying
(7x + -9)(6x + 8) = 0

Reorder the terms:
(-9 + 7x)(6x + 8) = 0

Reorder the terms:
(-9 + 7x)(8 + 6x) = 0

Multiply (-9 + 7x) * (8 + 6x)
(-9(8 + 6x) + 7x * (8 + 6x)) = 0
((8 * -9 + 6x * -9) + 7x * (8 + 6x)) = 0
((-72 + -54x) + 7x * (8 + 6x)) = 0
(-72 + -54x + (8 * 7x + 6x * 7x)) = 0
(-72 + -54x + (56x + 42x2)) = 0

Combine like terms: -54x + 56x = 2x
(-72 + 2x + 42x2) = 0

Solving
-72 + 2x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + x + 21x2) = 0

Factor a trinomial.
2((-4 + -3x)(9 + -7x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
Set the factor '(9 + -7x)' equal to zero and attempt to solve:

Simplifying
9 + -7x = 0

Solving
9 + -7x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -7x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -7x = 0 + -9
-7x = 0 + -9

Combine like terms: 0 + -9 = -9
-7x = -9

Divide each side by '-7'.
x = 1.285714286

Simplifying
x = 1.285714286
Solution
x = {-1.333333333, 1.285714286}

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