ax^4+bx^3+5x^2-3x+1=3x+7

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Solution for ax^4+bx^3+5x^2-3x+1=3x+7 equation: 


Simplifying
ax4 + bx3 + 5x2 + -3x + 1 = 3x + 7

Reorder the terms:
1 + ax4 + bx3 + -3x + 5x2 = 3x + 7

Reorder the terms:
1 + ax4 + bx3 + -3x + 5x2 = 7 + 3x

Solving
1 + ax4 + bx3 + -3x + 5x2 = 7 + 3x

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + ax4 + bx3 + -3x + -1 + 5x2 = 7 + -1 + 3x

Reorder the terms:
1 + -1 + ax4 + bx3 + -3x + 5x2 = 7 + -1 + 3x

Combine like terms: 1 + -1 = 0
0 + ax4 + bx3 + -3x + 5x2 = 7 + -1 + 3x
ax4 + bx3 + -3x + 5x2 = 7 + -1 + 3x

Combine like terms: 7 + -1 = 6
ax4 + bx3 + -3x + 5x2 = 6 + 3x

Add '-1bx3' to each side of the equation.
ax4 + bx3 + -3x + -1bx3 + 5x2 = 6 + -1bx3 + 3x

Reorder the terms:
ax4 + bx3 + -1bx3 + -3x + 5x2 = 6 + -1bx3 + 3x

Combine like terms: bx3 + -1bx3 = 0
ax4 + 0 + -3x + 5x2 = 6 + -1bx3 + 3x
ax4 + -3x + 5x2 = 6 + -1bx3 + 3x

Add '3x' to each side of the equation.
ax4 + -3x + 3x + 5x2 = 6 + -1bx3 + 3x + 3x

Combine like terms: -3x + 3x = 0
ax4 + 0 + 5x2 = 6 + -1bx3 + 3x + 3x
ax4 + 5x2 = 6 + -1bx3 + 3x + 3x

Combine like terms: 3x + 3x = 6x
ax4 + 5x2 = 6 + -1bx3 + 6x

Add '-5x2' to each side of the equation.
ax4 + 5x2 + -5x2 = 6 + -1bx3 + 6x + -5x2

Combine like terms: 5x2 + -5x2 = 0
ax4 + 0 = 6 + -1bx3 + 6x + -5x2
ax4 = 6 + -1bx3 + 6x + -5x2

Divide each side by 'x4'.
a = 6x-4 + -1bx-1 + 6x-3 + -5x-2

Simplifying
a = 6x-4 + -1bx-1 + 6x-3 + -5x-2

Reorder the terms:
a = -1bx-1 + 6x-4 + 6x-3 + -5x-2

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