(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((-3 + -4x)(9 + -7x)) = 0

Ignore the factor 2.

Subproblem 1
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

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 = {-0.75, 1.285714286}

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