4(3x-1)-2x(x-3)=24

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Solution for 4(3x-1)-2x(x-3)=24 equation:


Simplifying
4(3x + -1) + -2x(x + -3) = 24

Reorder the terms:
4(-1 + 3x) + -2x(x + -3) = 24
(-1 * 4 + 3x * 4) + -2x(x + -3) = 24
(-4 + 12x) + -2x(x + -3) = 24

Reorder the terms:
-4 + 12x + -2x(-3 + x) = 24
-4 + 12x + (-3 * -2x + x * -2x) = 24
-4 + 12x + (6x + -2x2) = 24

Combine like terms: 12x + 6x = 18x
-4 + 18x + -2x2 = 24

Solving
-4 + 18x + -2x2 = 24

Solving for variable 'x'.

Reorder the terms:
-4 + -24 + 18x + -2x2 = 24 + -24

Combine like terms: -4 + -24 = -28
-28 + 18x + -2x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-28 + 18x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + 9x + -1x2) = 0

Factor a trinomial.
2((-7 + x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {7, 2}

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