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

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


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

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

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

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

Combine like terms: -42x + 72x = 30x
(-54 + 30x + 56x2) = 0

Solving
-54 + 30x + 56x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + 15x + 28x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

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

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

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-1.285714286, 0.75}

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