4x^2-25=2x-5

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


Simplifying
4x2 + -25 = 2x + -5

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

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

Solving
-25 + 4x2 = -5 + 2x

Solving for variable 'x'.

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

Combine like terms: -25 + 5 = -20
-20 + -2x + 4x2 = -5 + 2x + 5 + -2x

Reorder the terms:
-20 + -2x + 4x2 = -5 + 5 + 2x + -2x

Combine like terms: -5 + 5 = 0
-20 + -2x + 4x2 = 0 + 2x + -2x
-20 + -2x + 4x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-20 + -2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -1x + 2x2) = 0

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

Ignore the factor 2.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 2.5}

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