4(x-5)(x-5)=36

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Solution for 4(x-5)(x-5)=36 equation: 


Simplifying
4(x + -5)(x + -5) = 36

Reorder the terms:
4(-5 + x)(x + -5) = 36

Reorder the terms:
4(-5 + x)(-5 + x) = 36

Multiply (-5 + x) * (-5 + x)
4(-5(-5 + x) + x(-5 + x)) = 36
4((-5 * -5 + x * -5) + x(-5 + x)) = 36
4((25 + -5x) + x(-5 + x)) = 36
4(25 + -5x + (-5 * x + x * x)) = 36
4(25 + -5x + (-5x + x2)) = 36

Combine like terms: -5x + -5x = -10x
4(25 + -10x + x2) = 36
(25 * 4 + -10x * 4 + x2 * 4) = 36
(100 + -40x + 4x2) = 36

Solving
100 + -40x + 4x2 = 36

Solving for variable 'x'.

Reorder the terms:
100 + -36 + -40x + 4x2 = 36 + -36

Combine like terms: 100 + -36 = 64
64 + -40x + 4x2 = 36 + -36

Combine like terms: 36 + -36 = 0
64 + -40x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(16 + -10x + x2) = 0

Factor a trinomial.
4((2 + -1x)(8 + -1x)) = 0

Ignore the factor 4.

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {2, 8}

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