25x^2-4=7x(5x-2)

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Solution for 25x^2-4=7x(5x-2) equation: 


Simplifying
25x2 + -4 = 7x(5x + -2)

Reorder the terms:
-4 + 25x2 = 7x(5x + -2)

Reorder the terms:
-4 + 25x2 = 7x(-2 + 5x)
-4 + 25x2 = (-2 * 7x + 5x * 7x)
-4 + 25x2 = (-14x + 35x2)

Solving
-4 + 25x2 = -14x + 35x2

Solving for variable 'x'.

Reorder the terms:
-4 + 14x + 25x2 + -35x2 = -14x + 35x2 + 14x + -35x2

Combine like terms: 25x2 + -35x2 = -10x2
-4 + 14x + -10x2 = -14x + 35x2 + 14x + -35x2

Reorder the terms:
-4 + 14x + -10x2 = -14x + 14x + 35x2 + -35x2

Combine like terms: -14x + 14x = 0
-4 + 14x + -10x2 = 0 + 35x2 + -35x2
-4 + 14x + -10x2 = 35x2 + -35x2

Combine like terms: 35x2 + -35x2 = 0
-4 + 14x + -10x2 = 0

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

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

Ignore the factor 2.

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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