4x^2+6x=7x^2-12x

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Solution for 4x^2+6x=7x^2-12x equation:


Simplifying
4x2 + 6x = 7x2 + -12x

Reorder the terms:
6x + 4x2 = 7x2 + -12x

Reorder the terms:
6x + 4x2 = -12x + 7x2

Solving
6x + 4x2 = -12x + 7x2

Solving for variable 'x'.

Reorder the terms:
6x + 12x + 4x2 + -7x2 = -12x + 7x2 + 12x + -7x2

Combine like terms: 6x + 12x = 18x
18x + 4x2 + -7x2 = -12x + 7x2 + 12x + -7x2

Combine like terms: 4x2 + -7x2 = -3x2
18x + -3x2 = -12x + 7x2 + 12x + -7x2

Reorder the terms:
18x + -3x2 = -12x + 12x + 7x2 + -7x2

Combine like terms: -12x + 12x = 0
18x + -3x2 = 0 + 7x2 + -7x2
18x + -3x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
18x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(6 + -1x) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

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 = {0, 6}

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