25(x^2+3x)=2(2x+6)

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Solution for 25(x^2+3x)=2(2x+6) equation: 


Simplifying
25(x2 + 3x) = 2(2x + 6)

Reorder the terms:
25(3x + x2) = 2(2x + 6)
(3x * 25 + x2 * 25) = 2(2x + 6)
(75x + 25x2) = 2(2x + 6)

Reorder the terms:
75x + 25x2 = 2(6 + 2x)
75x + 25x2 = (6 * 2 + 2x * 2)
75x + 25x2 = (12 + 4x)

Solving
75x + 25x2 = 12 + 4x

Solving for variable 'x'.

Reorder the terms:
-12 + 75x + -4x + 25x2 = 12 + 4x + -12 + -4x

Combine like terms: 75x + -4x = 71x
-12 + 71x + 25x2 = 12 + 4x + -12 + -4x

Reorder the terms:
-12 + 71x + 25x2 = 12 + -12 + 4x + -4x

Combine like terms: 12 + -12 = 0
-12 + 71x + 25x2 = 0 + 4x + -4x
-12 + 71x + 25x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-12 + 71x + 25x2 = 0

Factor a trinomial.
(-3 + -1x)(4 + -25x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(4 + -25x)' equal to zero and attempt to solve:

Simplifying
4 + -25x = 0

Solving
4 + -25x = 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 + -25x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -25x = 0 + -4
-25x = 0 + -4

Combine like terms: 0 + -4 = -4
-25x = -4

Divide each side by '-25'.
x = 0.16

Simplifying
x = 0.16
Solution
x = {-3, 0.16}

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