(4x+3)(4x+3)-25=0

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Solution for (4x+3)(4x+3)-25=0 equation: 


Simplifying
(4x + 3)(4x + 3) + -25 = 0

Reorder the terms:
(3 + 4x)(4x + 3) + -25 = 0

Reorder the terms:
(3 + 4x)(3 + 4x) + -25 = 0

Multiply (3 + 4x) * (3 + 4x)
(3(3 + 4x) + 4x * (3 + 4x)) + -25 = 0
((3 * 3 + 4x * 3) + 4x * (3 + 4x)) + -25 = 0
((9 + 12x) + 4x * (3 + 4x)) + -25 = 0
(9 + 12x + (3 * 4x + 4x * 4x)) + -25 = 0
(9 + 12x + (12x + 16x2)) + -25 = 0

Combine like terms: 12x + 12x = 24x
(9 + 24x + 16x2) + -25 = 0

Reorder the terms:
9 + -25 + 24x + 16x2 = 0

Combine like terms: 9 + -25 = -16
-16 + 24x + 16x2 = 0

Solving
-16 + 24x + 16x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 8.

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 '(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
Solution
x = {-2, 0.5}

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