3x^2+bx+10=a((x+3)(x+3))+c

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Solution for 3x^2+bx+10=a((x+3)(x+3))+c equation: 


Simplifying
3x2 + bx + 10 = a((x + 3)(x + 3)) + c

Reorder the terms:
10 + bx + 3x2 = a((x + 3)(x + 3)) + c

Reorder the terms:
10 + bx + 3x2 = a((3 + x)(x + 3)) + c

Reorder the terms:
10 + bx + 3x2 = a((3 + x)(3 + x)) + c

Multiply (3 + x) * (3 + x)
10 + bx + 3x2 = a((3(3 + x) + x(3 + x))) + c
10 + bx + 3x2 = a(((3 * 3 + x * 3) + x(3 + x))) + c
10 + bx + 3x2 = a(((9 + 3x) + x(3 + x))) + c
10 + bx + 3x2 = a((9 + 3x + (3 * x + x * x))) + c
10 + bx + 3x2 = a((9 + 3x + (3x + x2))) + c

Combine like terms: 3x + 3x = 6x
10 + bx + 3x2 = a((9 + 6x + x2)) + c
10 + bx + 3x2 = (9 * a + 6x * a + x2 * a) + c
10 + bx + 3x2 = (9a + 6ax + ax2) + c

Solving
10 + bx + 3x2 = 9a + 6ax + ax2 + c

Solving for variable 'b'.

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

Add '-10' to each side of the equation.
10 + bx + -10 + 3x2 = 9a + 6ax + ax2 + -10 + c

Reorder the terms:
10 + -10 + bx + 3x2 = 9a + 6ax + ax2 + -10 + c

Combine like terms: 10 + -10 = 0
0 + bx + 3x2 = 9a + 6ax + ax2 + -10 + c
bx + 3x2 = 9a + 6ax + ax2 + -10 + c

Reorder the terms:
bx + 3x2 = -10 + 9a + 6ax + ax2 + c

Add '-3x2' to each side of the equation.
bx + 3x2 + -3x2 = -10 + 9a + 6ax + ax2 + c + -3x2

Combine like terms: 3x2 + -3x2 = 0
bx + 0 = -10 + 9a + 6ax + ax2 + c + -3x2
bx = -10 + 9a + 6ax + ax2 + c + -3x2

Divide each side by 'x'.
b = -10x-1 + 9ax-1 + 6a + ax + cx-1 + -3x

Simplifying
b = -10x-1 + 9ax-1 + 6a + ax + cx-1 + -3x

Reorder the terms:
b = 6a + 9ax-1 + ax + cx-1 + -10x-1 + -3x

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