9(x-6)(x+1)=0

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Solution for 9(x-6)(x+1)=0 equation:


Simplifying
9(x + -6)(x + 1) = 0

Reorder the terms:
9(-6 + x)(x + 1) = 0

Reorder the terms:
9(-6 + x)(1 + x) = 0

Multiply (-6 + x) * (1 + x)
9(-6(1 + x) + x(1 + x)) = 0
9((1 * -6 + x * -6) + x(1 + x)) = 0
9((-6 + -6x) + x(1 + x)) = 0
9(-6 + -6x + (1 * x + x * x)) = 0
9(-6 + -6x + (1x + x2)) = 0

Combine like terms: -6x + 1x = -5x
9(-6 + -5x + x2) = 0
(-6 * 9 + -5x * 9 + x2 * 9) = 0
(-54 + -45x + 9x2) = 0

Solving
-54 + -45x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-6 + -5x + x2) = 0

Factor a trinomial.
9((-1 + -1x)(6 + -1x)) = 0

Ignore the factor 9.

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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {-1, 6}

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