12(25x^2-10x+1)+5=-19(5x-1)

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Solution for 12(25x^2-10x+1)+5=-19(5x-1) equation: 


Simplifying
12(25x2 + -10x + 1) + 5 = -19(5x + -1)

Reorder the terms:
12(1 + -10x + 25x2) + 5 = -19(5x + -1)
(1 * 12 + -10x * 12 + 25x2 * 12) + 5 = -19(5x + -1)
(12 + -120x + 300x2) + 5 = -19(5x + -1)

Reorder the terms:
12 + 5 + -120x + 300x2 = -19(5x + -1)

Combine like terms: 12 + 5 = 17
17 + -120x + 300x2 = -19(5x + -1)

Reorder the terms:
17 + -120x + 300x2 = -19(-1 + 5x)
17 + -120x + 300x2 = (-1 * -19 + 5x * -19)
17 + -120x + 300x2 = (19 + -95x)

Solving
17 + -120x + 300x2 = 19 + -95x

Solving for variable 'x'.

Reorder the terms:
17 + -19 + -120x + 95x + 300x2 = 19 + -95x + -19 + 95x

Combine like terms: 17 + -19 = -2
-2 + -120x + 95x + 300x2 = 19 + -95x + -19 + 95x

Combine like terms: -120x + 95x = -25x
-2 + -25x + 300x2 = 19 + -95x + -19 + 95x

Reorder the terms:
-2 + -25x + 300x2 = 19 + -19 + -95x + 95x

Combine like terms: 19 + -19 = 0
-2 + -25x + 300x2 = 0 + -95x + 95x
-2 + -25x + 300x2 = -95x + 95x

Combine like terms: -95x + 95x = 0
-2 + -25x + 300x2 = 0

Factor a trinomial.
(-1 + -20x)(2 + -15x) = 0


Subproblem 1
Set the factor '(-1 + -20x)' equal to zero and attempt to solve:

Simplifying
-1 + -20x = 0

Solving
-1 + -20x = 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 + -20x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -20x = 0 + 1
-20x = 0 + 1

Combine like terms: 0 + 1 = 1
-20x = 1

Divide each side by '-20'.
x = -0.05

Simplifying
x = -0.05

Subproblem 2
Set the factor '(2 + -15x)' equal to zero and attempt to solve:

Simplifying
2 + -15x = 0

Solving
2 + -15x = 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 + -15x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -15x = 0 + -2
-15x = 0 + -2

Combine like terms: 0 + -2 = -2
-15x = -2

Divide each side by '-15'.
x = 0.1333333333

Simplifying
x = 0.1333333333
Solution
x = {-0.05, 0.1333333333}

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