25x^2-4-(2x-5)(5x+2)=0

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Solution for 25x^2-4-(2x-5)(5x+2)=0 equation: 


Simplifying
25x2 + -4 + -1(2x + -5)(5x + 2) = 0

Reorder the terms:
25x2 + -4 + -1(-5 + 2x)(5x + 2) = 0

Reorder the terms:
25x2 + -4 + -1(-5 + 2x)(2 + 5x) = 0

Multiply (-5 + 2x) * (2 + 5x)
25x2 + -4 + -1(-5(2 + 5x) + 2x * (2 + 5x)) = 0
25x2 + -4 + -1((2 * -5 + 5x * -5) + 2x * (2 + 5x)) = 0
25x2 + -4 + -1((-10 + -25x) + 2x * (2 + 5x)) = 0
25x2 + -4 + -1(-10 + -25x + (2 * 2x + 5x * 2x)) = 0
25x2 + -4 + -1(-10 + -25x + (4x + 10x2)) = 0

Combine like terms: -25x + 4x = -21x
25x2 + -4 + -1(-10 + -21x + 10x2) = 0
25x2 + -4 + (-10 * -1 + -21x * -1 + 10x2 * -1) = 0
25x2 + -4 + (10 + 21x + -10x2) = 0

Reorder the terms:
-4 + 10 + 21x + 25x2 + -10x2 = 0

Combine like terms: -4 + 10 = 6
6 + 21x + 25x2 + -10x2 = 0

Combine like terms: 25x2 + -10x2 = 15x2
6 + 21x + 15x2 = 0

Solving
6 + 21x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 7x + 5x2) = 0

Factor a trinomial.
3((1 + x)(2 + 5x)) = 0

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
Set the factor '(2 + 5x)' equal to zero and attempt to solve:

Simplifying
2 + 5x = 0

Solving
2 + 5x = 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 + 5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5x = 0 + -2
5x = 0 + -2

Combine like terms: 0 + -2 = -2
5x = -2

Divide each side by '5'.
x = -0.4

Simplifying
x = -0.4
Solution
x = {-1, -0.4}

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