25X^2-4+(5X+2)(4X-7)=0

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Solution for 25X^2-4+(5X+2)(4X-7)=0 equation: 


Simplifying
25X2 + -4 + (5X + 2)(4X + -7) = 0

Reorder the terms:
25X2 + -4 + (2 + 5X)(4X + -7) = 0

Reorder the terms:
25X2 + -4 + (2 + 5X)(-7 + 4X) = 0

Multiply (2 + 5X) * (-7 + 4X)
25X2 + -4 + (2(-7 + 4X) + 5X * (-7 + 4X)) = 0
25X2 + -4 + ((-7 * 2 + 4X * 2) + 5X * (-7 + 4X)) = 0
25X2 + -4 + ((-14 + 8X) + 5X * (-7 + 4X)) = 0
25X2 + -4 + (-14 + 8X + (-7 * 5X + 4X * 5X)) = 0
25X2 + -4 + (-14 + 8X + (-35X + 20X2)) = 0

Combine like terms: 8X + -35X = -27X
25X2 + -4 + (-14 + -27X + 20X2) = 0

Reorder the terms:
-4 + -14 + -27X + 25X2 + 20X2 = 0

Combine like terms: -4 + -14 = -18
-18 + -27X + 25X2 + 20X2 = 0

Combine like terms: 25X2 + 20X2 = 45X2
-18 + -27X + 45X2 = 0

Solving
-18 + -27X + 45X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-2 + -3X + 5X2) = 0

Factor a trinomial.
9((-2 + -5X)(1 + -1X)) = 0

Ignore the factor 9.

Subproblem 1
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

Subproblem 2
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
Solution
X = {-0.4, 1}

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