6x^2=-15+21x

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Solution for 6x^2=-15+21x equation:


Simplifying
6x2 = -15 + 21x

Solving
6x2 = -15 + 21x

Solving for variable 'x'.

Reorder the terms:
15 + -21x + 6x2 = -15 + 21x + 15 + -21x

Reorder the terms:
15 + -21x + 6x2 = -15 + 15 + 21x + -21x

Combine like terms: -15 + 15 = 0
15 + -21x + 6x2 = 0 + 21x + -21x
15 + -21x + 6x2 = 21x + -21x

Combine like terms: 21x + -21x = 0
15 + -21x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -7x + 2x2) = 0

Factor a trinomial.
3((1 + -1x)(5 + -2x)) = 0

Ignore the factor 3.

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 '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Solution

x = {1, 2.5}

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