11(a-2)-4(2-a)-2(1-4a)=19(a-3)

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Solution for 11(a-2)-4(2-a)-2(1-4a)=19(a-3) equation: 


Simplifying
11(a + -2) + -4(2 + -1a) + -2(1 + -4a) = 19(a + -3)

Reorder the terms:
11(-2 + a) + -4(2 + -1a) + -2(1 + -4a) = 19(a + -3)
(-2 * 11 + a * 11) + -4(2 + -1a) + -2(1 + -4a) = 19(a + -3)
(-22 + 11a) + -4(2 + -1a) + -2(1 + -4a) = 19(a + -3)
-22 + 11a + (2 * -4 + -1a * -4) + -2(1 + -4a) = 19(a + -3)
-22 + 11a + (-8 + 4a) + -2(1 + -4a) = 19(a + -3)
-22 + 11a + -8 + 4a + (1 * -2 + -4a * -2) = 19(a + -3)
-22 + 11a + -8 + 4a + (-2 + 8a) = 19(a + -3)

Reorder the terms:
-22 + -8 + -2 + 11a + 4a + 8a = 19(a + -3)

Combine like terms: -22 + -8 = -30
-30 + -2 + 11a + 4a + 8a = 19(a + -3)

Combine like terms: -30 + -2 = -32
-32 + 11a + 4a + 8a = 19(a + -3)

Combine like terms: 11a + 4a = 15a
-32 + 15a + 8a = 19(a + -3)

Combine like terms: 15a + 8a = 23a
-32 + 23a = 19(a + -3)

Reorder the terms:
-32 + 23a = 19(-3 + a)
-32 + 23a = (-3 * 19 + a * 19)
-32 + 23a = (-57 + 19a)

Solving
-32 + 23a = -57 + 19a

Solving for variable 'a'.

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

Add '-19a' to each side of the equation.
-32 + 23a + -19a = -57 + 19a + -19a

Combine like terms: 23a + -19a = 4a
-32 + 4a = -57 + 19a + -19a

Combine like terms: 19a + -19a = 0
-32 + 4a = -57 + 0
-32 + 4a = -57

Add '32' to each side of the equation.
-32 + 32 + 4a = -57 + 32

Combine like terms: -32 + 32 = 0
0 + 4a = -57 + 32
4a = -57 + 32

Combine like terms: -57 + 32 = -25
4a = -25

Divide each side by '4'.
a = -6.25

Simplifying
a = -6.25

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