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

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


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

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

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

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

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

Solving
9 + -24x + 16x2 = x

Solving for variable 'x'.

Reorder the terms:
9 + -24x + -1x + 16x2 = x + -1x

Combine like terms: -24x + -1x = -25x
9 + -25x + 16x2 = x + -1x

Combine like terms: x + -1x = 0
9 + -25x + 16x2 = 0

Factor a trinomial.
(9 + -16x)(1 + -1x) = 0


Subproblem 1
Set the factor '(9 + -16x)' equal to zero and attempt to solve:

Simplifying
9 + -16x = 0

Solving
9 + -16x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -16x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -16x = 0 + -9
-16x = 0 + -9

Combine like terms: 0 + -9 = -9
-16x = -9

Divide each side by '-16'.
x = 0.5625

Simplifying
x = 0.5625

Subproblem 2
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
Solution
x = {0.5625, 1}

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