4(x-3)(x-3)=1

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Solution for 4(x-3)(x-3)=1 equation: 


Simplifying
4(x + -3)(x + -3) = 1

Reorder the terms:
4(-3 + x)(x + -3) = 1

Reorder the terms:
4(-3 + x)(-3 + x) = 1

Multiply (-3 + x) * (-3 + x)
4(-3(-3 + x) + x(-3 + x)) = 1
4((-3 * -3 + x * -3) + x(-3 + x)) = 1
4((9 + -3x) + x(-3 + x)) = 1
4(9 + -3x + (-3 * x + x * x)) = 1
4(9 + -3x + (-3x + x2)) = 1

Combine like terms: -3x + -3x = -6x
4(9 + -6x + x2) = 1
(9 * 4 + -6x * 4 + x2 * 4) = 1
(36 + -24x + 4x2) = 1

Solving
36 + -24x + 4x2 = 1

Solving for variable 'x'.

Reorder the terms:
36 + -1 + -24x + 4x2 = 1 + -1

Combine like terms: 36 + -1 = 35
35 + -24x + 4x2 = 1 + -1

Combine like terms: 1 + -1 = 0
35 + -24x + 4x2 = 0

Factor a trinomial.
(5 + -2x)(7 + -2x) = 0


Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5

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

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {2.5, 3.5}

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