(2a+3)x^2+6bx+5c=5x^2-18x-35

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Solution for (2a+3)x^2+6bx+5c=5x^2-18x-35 equation: 


Simplifying
(2a + 3) * x2 + 6bx + 5c = 5x2 + -18x + -35

Reorder the terms:
(3 + 2a) * x2 + 6bx + 5c = 5x2 + -18x + -35

Reorder the terms for easier multiplication:
x2(3 + 2a) + 6bx + 5c = 5x2 + -18x + -35
(3 * x2 + 2a * x2) + 6bx + 5c = 5x2 + -18x + -35

Reorder the terms:
(2ax2 + 3x2) + 6bx + 5c = 5x2 + -18x + -35
(2ax2 + 3x2) + 6bx + 5c = 5x2 + -18x + -35

Reorder the terms:
2ax2 + 6bx + 5c + 3x2 = 5x2 + -18x + -35

Reorder the terms:
2ax2 + 6bx + 5c + 3x2 = -35 + -18x + 5x2

Solving
2ax2 + 6bx + 5c + 3x2 = -35 + -18x + 5x2

Solving for variable 'a'.

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

Add '-6bx' to each side of the equation.
2ax2 + 6bx + 5c + -6bx + 3x2 = -35 + -18x + -6bx + 5x2

Reorder the terms:
2ax2 + 6bx + -6bx + 5c + 3x2 = -35 + -18x + -6bx + 5x2

Combine like terms: 6bx + -6bx = 0
2ax2 + 0 + 5c + 3x2 = -35 + -18x + -6bx + 5x2
2ax2 + 5c + 3x2 = -35 + -18x + -6bx + 5x2

Reorder the terms:
2ax2 + 5c + 3x2 = -35 + -6bx + -18x + 5x2

Add '-5c' to each side of the equation.
2ax2 + 5c + -5c + 3x2 = -35 + -6bx + -18x + -5c + 5x2

Combine like terms: 5c + -5c = 0
2ax2 + 0 + 3x2 = -35 + -6bx + -18x + -5c + 5x2
2ax2 + 3x2 = -35 + -6bx + -18x + -5c + 5x2

Reorder the terms:
2ax2 + 3x2 = -35 + -6bx + -5c + -18x + 5x2

Add '-3x2' to each side of the equation.
2ax2 + 3x2 + -3x2 = -35 + -6bx + -5c + -18x + 5x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
2ax2 + 0 = -35 + -6bx + -5c + -18x + 5x2 + -3x2
2ax2 = -35 + -6bx + -5c + -18x + 5x2 + -3x2

Combine like terms: 5x2 + -3x2 = 2x2
2ax2 = -35 + -6bx + -5c + -18x + 2x2

Divide each side by '2x2'.
a = -17.5x-2 + -3bx-1 + -2.5cx-2 + -9x-1 + 1

Simplifying
a = -17.5x-2 + -3bx-1 + -2.5cx-2 + -9x-1 + 1

Reorder the terms:
a = 1 + -3bx-1 + -2.5cx-2 + -17.5x-2 + -9x-1

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