(3x-4)(3x-4)=25

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Solution for (3x-4)(3x-4)=25 equation: 


Simplifying
(3x + -4)(3x + -4) = 25

Reorder the terms:
(-4 + 3x)(3x + -4) = 25

Reorder the terms:
(-4 + 3x)(-4 + 3x) = 25

Multiply (-4 + 3x) * (-4 + 3x)
(-4(-4 + 3x) + 3x * (-4 + 3x)) = 25
((-4 * -4 + 3x * -4) + 3x * (-4 + 3x)) = 25
((16 + -12x) + 3x * (-4 + 3x)) = 25
(16 + -12x + (-4 * 3x + 3x * 3x)) = 25
(16 + -12x + (-12x + 9x2)) = 25

Combine like terms: -12x + -12x = -24x
(16 + -24x + 9x2) = 25

Solving
16 + -24x + 9x2 = 25

Solving for variable 'x'.

Reorder the terms:
16 + -25 + -24x + 9x2 = 25 + -25

Combine like terms: 16 + -25 = -9
-9 + -24x + 9x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-9 + -24x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -8x + 3x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.3333333333, 3}

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