3x(x+1)=x^2-7x+12

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Solution for 3x(x+1)=x^2-7x+12 equation:


Simplifying
3x(x + 1) = x2 + -7x + 12

Reorder the terms:
3x(1 + x) = x2 + -7x + 12
(1 * 3x + x * 3x) = x2 + -7x + 12
(3x + 3x2) = x2 + -7x + 12

Reorder the terms:
3x + 3x2 = 12 + -7x + x2

Solving
3x + 3x2 = 12 + -7x + x2

Solving for variable 'x'.

Reorder the terms:
-12 + 3x + 7x + 3x2 + -1x2 = 12 + -7x + x2 + -12 + 7x + -1x2

Combine like terms: 3x + 7x = 10x
-12 + 10x + 3x2 + -1x2 = 12 + -7x + x2 + -12 + 7x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-12 + 10x + 2x2 = 12 + -7x + x2 + -12 + 7x + -1x2

Reorder the terms:
-12 + 10x + 2x2 = 12 + -12 + -7x + 7x + x2 + -1x2

Combine like terms: 12 + -12 = 0
-12 + 10x + 2x2 = 0 + -7x + 7x + x2 + -1x2
-12 + 10x + 2x2 = -7x + 7x + x2 + -1x2

Combine like terms: -7x + 7x = 0
-12 + 10x + 2x2 = 0 + x2 + -1x2
-12 + 10x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 5x + x2) = 0

Factor a trinomial.
2((-6 + -1x)(1 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

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

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 = {-6, 1}

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