(4x-3)(4x-3)-49=0

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Solution for (4x-3)(4x-3)-49=0 equation: 


Simplifying
(4x + -3)(4x + -3) + -49 = 0

Reorder the terms:
(-3 + 4x)(4x + -3) + -49 = 0

Reorder the terms:
(-3 + 4x)(-3 + 4x) + -49 = 0

Multiply (-3 + 4x) * (-3 + 4x)
(-3(-3 + 4x) + 4x * (-3 + 4x)) + -49 = 0
((-3 * -3 + 4x * -3) + 4x * (-3 + 4x)) + -49 = 0
((9 + -12x) + 4x * (-3 + 4x)) + -49 = 0
(9 + -12x + (-3 * 4x + 4x * 4x)) + -49 = 0
(9 + -12x + (-12x + 16x2)) + -49 = 0

Combine like terms: -12x + -12x = -24x
(9 + -24x + 16x2) + -49 = 0

Reorder the terms:
9 + -49 + -24x + 16x2 = 0

Combine like terms: 9 + -49 = -40
-40 + -24x + 16x2 = 0

Solving
-40 + -24x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-5 + -3x + 2x2) = 0

Factor a trinomial.
8((-1 + -1x)(5 + -2x)) = 0

Ignore the factor 8.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-1, 2.5}

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