125-5(2x-3)(2x-3)=0

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Solution for 125-5(2x-3)(2x-3)=0 equation: 


Simplifying
125 + -5(2x + -3)(2x + -3) = 0

Reorder the terms:
125 + -5(-3 + 2x)(2x + -3) = 0

Reorder the terms:
125 + -5(-3 + 2x)(-3 + 2x) = 0

Multiply (-3 + 2x) * (-3 + 2x)
125 + -5(-3(-3 + 2x) + 2x * (-3 + 2x)) = 0
125 + -5((-3 * -3 + 2x * -3) + 2x * (-3 + 2x)) = 0
125 + -5((9 + -6x) + 2x * (-3 + 2x)) = 0
125 + -5(9 + -6x + (-3 * 2x + 2x * 2x)) = 0
125 + -5(9 + -6x + (-6x + 4x2)) = 0

Combine like terms: -6x + -6x = -12x
125 + -5(9 + -12x + 4x2) = 0
125 + (9 * -5 + -12x * -5 + 4x2 * -5) = 0
125 + (-45 + 60x + -20x2) = 0

Combine like terms: 125 + -45 = 80
80 + 60x + -20x2 = 0

Solving
80 + 60x + -20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '20'.
20(4 + 3x + -1x2) = 0

Factor a trinomial.
20((4 + -1x)(1 + x)) = 0

Ignore the factor 20.

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {4, -1}

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