2(x+3)(x-7)=0

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Solution for 2(x+3)(x-7)=0 equation:


Simplifying
2(x + 3)(x + -7) = 0

Reorder the terms:
2(3 + x)(x + -7) = 0

Reorder the terms:
2(3 + x)(-7 + x) = 0

Multiply (3 + x) * (-7 + x)
2(3(-7 + x) + x(-7 + x)) = 0
2((-7 * 3 + x * 3) + x(-7 + x)) = 0
2((-21 + 3x) + x(-7 + x)) = 0
2(-21 + 3x + (-7 * x + x * x)) = 0
2(-21 + 3x + (-7x + x2)) = 0

Combine like terms: 3x + -7x = -4x
2(-21 + -4x + x2) = 0
(-21 * 2 + -4x * 2 + x2 * 2) = 0
(-42 + -8x + 2x2) = 0

Solving
-42 + -8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -4x + x2) = 0

Factor a trinomial.
2((-3 + -1x)(7 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3

Subproblem 2

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Solution

x = {-3, 7}

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