25x^2+30x+9=9-6x+4x^2

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Solution for 25x^2+30x+9=9-6x+4x^2 equation:


Simplifying
25x2 + 30x + 9 = 9 + -6x + 4x2

Reorder the terms:
9 + 30x + 25x2 = 9 + -6x + 4x2

Add '-9' to each side of the equation.
9 + 30x + -9 + 25x2 = 9 + -6x + -9 + 4x2

Reorder the terms:
9 + -9 + 30x + 25x2 = 9 + -6x + -9 + 4x2

Combine like terms: 9 + -9 = 0
0 + 30x + 25x2 = 9 + -6x + -9 + 4x2
30x + 25x2 = 9 + -6x + -9 + 4x2

Reorder the terms:
30x + 25x2 = 9 + -9 + -6x + 4x2

Combine like terms: 9 + -9 = 0
30x + 25x2 = 0 + -6x + 4x2
30x + 25x2 = -6x + 4x2

Solving
30x + 25x2 = -6x + 4x2

Solving for variable 'x'.

Reorder the terms:
30x + 6x + 25x2 + -4x2 = -6x + 4x2 + 6x + -4x2

Combine like terms: 30x + 6x = 36x
36x + 25x2 + -4x2 = -6x + 4x2 + 6x + -4x2

Combine like terms: 25x2 + -4x2 = 21x2
36x + 21x2 = -6x + 4x2 + 6x + -4x2

Reorder the terms:
36x + 21x2 = -6x + 6x + 4x2 + -4x2

Combine like terms: -6x + 6x = 0
36x + 21x2 = 0 + 4x2 + -4x2
36x + 21x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
36x + 21x2 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(12 + 7x) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(12 + 7x)' equal to zero and attempt to solve: Simplifying 12 + 7x = 0 Solving 12 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + 7x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 7x = 0 + -12 7x = 0 + -12 Combine like terms: 0 + -12 = -12 7x = -12 Divide each side by '7'. x = -1.714285714 Simplifying x = -1.714285714

Solution

x = {0, -1.714285714}

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