15x(x-1)=-3(5-x)+12x

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Solution for 15x(x-1)=-3(5-x)+12x equation:


Simplifying
15x(x + -1) = -3(5 + -1x) + 12x

Reorder the terms:
15x(-1 + x) = -3(5 + -1x) + 12x
(-1 * 15x + x * 15x) = -3(5 + -1x) + 12x
(-15x + 15x2) = -3(5 + -1x) + 12x
-15x + 15x2 = (5 * -3 + -1x * -3) + 12x
-15x + 15x2 = (-15 + 3x) + 12x

Combine like terms: 3x + 12x = 15x
-15x + 15x2 = -15 + 15x

Solving
-15x + 15x2 = -15 + 15x

Solving for variable 'x'.

Reorder the terms:
15 + -15x + -15x + 15x2 = -15 + 15x + 15 + -15x

Combine like terms: -15x + -15x = -30x
15 + -30x + 15x2 = -15 + 15x + 15 + -15x

Reorder the terms:
15 + -30x + 15x2 = -15 + 15 + 15x + -15x

Combine like terms: -15 + 15 = 0
15 + -30x + 15x2 = 0 + 15x + -15x
15 + -30x + 15x2 = 15x + -15x

Combine like terms: 15x + -15x = 0
15 + -30x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(1 + -2x + x2) = 0

Factor a trinomial.
15((1 + -1x)(1 + -1x)) = 0

Ignore the factor 15.

Subproblem 1

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

Subproblem 2

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

Solution

x = {1, 1}

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