(2x+9)(6x-7)=0

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Solution for (2x+9)(6x-7)=0 equation: 


Simplifying
(2x + 9)(6x + -7) = 0

Reorder the terms:
(9 + 2x)(6x + -7) = 0

Reorder the terms:
(9 + 2x)(-7 + 6x) = 0

Multiply (9 + 2x) * (-7 + 6x)
(9(-7 + 6x) + 2x * (-7 + 6x)) = 0
((-7 * 9 + 6x * 9) + 2x * (-7 + 6x)) = 0
((-63 + 54x) + 2x * (-7 + 6x)) = 0
(-63 + 54x + (-7 * 2x + 6x * 2x)) = 0
(-63 + 54x + (-14x + 12x2)) = 0

Combine like terms: 54x + -14x = 40x
(-63 + 40x + 12x2) = 0

Solving
-63 + 40x + 12x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + -2x)(7 + -6x) = 0


Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 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 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5

Subproblem 2
Set the factor '(7 + -6x)' equal to zero and attempt to solve:

Simplifying
7 + -6x = 0

Solving
7 + -6x = 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 + -6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x = 0 + -7
-6x = 0 + -7

Combine like terms: 0 + -7 = -7
-6x = -7

Divide each side by '-6'.
x = 1.166666667

Simplifying
x = 1.166666667
Solution
x = {-4.5, 1.166666667}

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