a(x+5)+b(x-2)=c(x-1)

Solution for a(x+5)+b(x-2)=c(x-1) equation:

Simplifying
a(x + 5) + b(x + -2) = c(x + -1)

Reorder the terms:
a(5 + x) + b(x + -2) = c(x + -1)
(5 * a + x * a) + b(x + -2) = c(x + -1)
(5a + ax) + b(x + -2) = c(x + -1)

Reorder the terms:
5a + ax + b(-2 + x) = c(x + -1)
5a + ax + (-2 * b + x * b) = c(x + -1)
5a + ax + (-2b + bx) = c(x + -1)

Reorder the terms:
5a + ax + -2b + bx = c(-1 + x)
5a + ax + -2b + bx = (-1 * c + x * c)
5a + ax + -2b + bx = (-1c + cx)

Solving
5a + ax + -2b + bx = -1c + cx

Solving for variable 'a'.

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

Add '2b' to each side of the equation.
5a + ax + -2b + 2b + bx = -1c + 2b + cx

Combine like terms: -2b + 2b = 0
5a + ax + 0 + bx = -1c + 2b + cx
5a + ax + bx = -1c + 2b + cx

Reorder the terms:
5a + ax + bx = 2b + -1c + cx

Add '-1bx' to each side of the equation.
5a + ax + bx + -1bx = 2b + -1c + -1bx + cx

Combine like terms: bx + -1bx = 0
5a + ax + 0 = 2b + -1c + -1bx + cx
5a + ax = 2b + -1c + -1bx + cx

Reorder the terms:
5a + ax = 2b + -1bx + -1c + cx

Reorder the terms:
5a + ax + -2b + bx + c + -1cx = 2b + -2b + -1bx + bx + -1c + c + cx + -1cx

Combine like terms: 2b + -2b = 0
5a + ax + -2b + bx + c + -1cx = 0 + -1bx + bx + -1c + c + cx + -1cx
5a + ax + -2b + bx + c + -1cx = -1bx + bx + -1c + c + cx + -1cx

Combine like terms: -1bx + bx = 0
5a + ax + -2b + bx + c + -1cx = 0 + -1c + c + cx + -1cx
5a + ax + -2b + bx + c + -1cx = -1c + c + cx + -1cx

Combine like terms: -1c + c = 0
5a + ax + -2b + bx + c + -1cx = 0 + cx + -1cx
5a + ax + -2b + bx + c + -1cx = cx + -1cx

Combine like terms: cx + -1cx = 0
5a + ax + -2b + bx + c + -1cx = 0

The solution to this equation could not be determined.