(5x+6)(5x-9)=0

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Solution for (5x+6)(5x-9)=0 equation: 


Simplifying
(5x + 6)(5x + -9) = 0

Reorder the terms:
(6 + 5x)(5x + -9) = 0

Reorder the terms:
(6 + 5x)(-9 + 5x) = 0

Multiply (6 + 5x) * (-9 + 5x)
(6(-9 + 5x) + 5x * (-9 + 5x)) = 0
((-9 * 6 + 5x * 6) + 5x * (-9 + 5x)) = 0
((-54 + 30x) + 5x * (-9 + 5x)) = 0
(-54 + 30x + (-9 * 5x + 5x * 5x)) = 0
(-54 + 30x + (-45x + 25x2)) = 0

Combine like terms: 30x + -45x = -15x
(-54 + -15x + 25x2) = 0

Solving
-54 + -15x + 25x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -5x)(9 + -5x) = 0


Subproblem 1
Set the factor '(-6 + -5x)' equal to zero and attempt to solve:

Simplifying
-6 + -5x = 0

Solving
-6 + -5x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -5x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5x = 0 + 6
-5x = 0 + 6

Combine like terms: 0 + 6 = 6
-5x = 6

Divide each side by '-5'.
x = -1.2

Simplifying
x = -1.2

Subproblem 2
Set the factor '(9 + -5x)' equal to zero and attempt to solve:

Simplifying
9 + -5x = 0

Solving
9 + -5x = 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 + -5x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5x = 0 + -9
-5x = 0 + -9

Combine like terms: 0 + -9 = -9
-5x = -9

Divide each side by '-5'.
x = 1.8

Simplifying
x = 1.8
Solution
x = {-1.2, 1.8}

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