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

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


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

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

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

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

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

Solving
9 + -24x + 16x2 = 25

Solving for variable 'x'.

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

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

Combine like terms: 25 + -25 = 0
-16 + -24x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-2 + -3x + 2x2) = 0

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

Ignore the factor 8.

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 2
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
Solution
x = {-0.5, 2}

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