(5-6x)(-5+9x)=-4

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Solution for (5-6x)(-5+9x)=-4 equation: 


Simplifying
(5 + -6x)(-5 + 9x) = -4

Multiply (5 + -6x) * (-5 + 9x)
(5(-5 + 9x) + -6x * (-5 + 9x)) = -4
((-5 * 5 + 9x * 5) + -6x * (-5 + 9x)) = -4
((-25 + 45x) + -6x * (-5 + 9x)) = -4
(-25 + 45x + (-5 * -6x + 9x * -6x)) = -4
(-25 + 45x + (30x + -54x2)) = -4

Combine like terms: 45x + 30x = 75x
(-25 + 75x + -54x2) = -4

Solving
-25 + 75x + -54x2 = -4

Solving for variable 'x'.

Reorder the terms:
-25 + 4 + 75x + -54x2 = -4 + 4

Combine like terms: -25 + 4 = -21
-21 + 75x + -54x2 = -4 + 4

Combine like terms: -4 + 4 = 0
-21 + 75x + -54x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 25x + -18x2) = 0

Factor a trinomial.
3((-1 + x)(7 + -18x)) = 0

Ignore the factor 3.

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

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

Add '1' to each side of the equation.
-1 + 1 + x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0 + 1
x = 0 + 1

Combine like terms: 0 + 1 = 1
x = 1

Simplifying
x = 1

Subproblem 2
Set the factor '(7 + -18x)' equal to zero and attempt to solve:

Simplifying
7 + -18x = 0

Solving
7 + -18x = 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 + -18x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -18x = 0 + -7
-18x = 0 + -7

Combine like terms: 0 + -7 = -7
-18x = -7

Divide each side by '-18'.
x = 0.3888888889

Simplifying
x = 0.3888888889
Solution
x = {1, 0.3888888889}

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