(3x-5)(3x-4)=56

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Solution for (3x-5)(3x-4)=56 equation: 


Simplifying
(3x + -5)(3x + -4) = 56

Reorder the terms:
(-5 + 3x)(3x + -4) = 56

Reorder the terms:
(-5 + 3x)(-4 + 3x) = 56

Multiply (-5 + 3x) * (-4 + 3x)
(-5(-4 + 3x) + 3x * (-4 + 3x)) = 56
((-4 * -5 + 3x * -5) + 3x * (-4 + 3x)) = 56
((20 + -15x) + 3x * (-4 + 3x)) = 56
(20 + -15x + (-4 * 3x + 3x * 3x)) = 56
(20 + -15x + (-12x + 9x2)) = 56

Combine like terms: -15x + -12x = -27x
(20 + -27x + 9x2) = 56

Solving
20 + -27x + 9x2 = 56

Solving for variable 'x'.

Reorder the terms:
20 + -56 + -27x + 9x2 = 56 + -56

Combine like terms: 20 + -56 = -36
-36 + -27x + 9x2 = 56 + -56

Combine like terms: 56 + -56 = 0
-36 + -27x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-4 + -3x + x2) = 0

Factor a trinomial.
9((-1 + -1x)(4 + -1x)) = 0

Ignore the factor 9.

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

Divide each side by '-1'.
x = -1

Simplifying
x = -1

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1, 4}

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