0=(15x+2)(x+7)

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Solution for 0=(15x+2)(x+7) equation:


Simplifying
0 = (15x + 2)(x + 7)

Reorder the terms:
0 = (2 + 15x)(x + 7)

Reorder the terms:
0 = (2 + 15x)(7 + x)

Multiply (2 + 15x) * (7 + x)
0 = (2(7 + x) + 15x * (7 + x))
0 = ((7 * 2 + x * 2) + 15x * (7 + x))
0 = ((14 + 2x) + 15x * (7 + x))
0 = (14 + 2x + (7 * 15x + x * 15x))
0 = (14 + 2x + (105x + 15x2))

Combine like terms: 2x + 105x = 107x
0 = (14 + 107x + 15x2)

Solving
0 = 14 + 107x + 15x2

Solving for variable 'x'.

Combine like terms: 0 + -14 = -14
-14 + -107x + -15x2 = 14 + 107x + 15x2 + -14 + -107x + -15x2

Reorder the terms:
-14 + -107x + -15x2 = 14 + -14 + 107x + -107x + 15x2 + -15x2

Combine like terms: 14 + -14 = 0
-14 + -107x + -15x2 = 0 + 107x + -107x + 15x2 + -15x2
-14 + -107x + -15x2 = 107x + -107x + 15x2 + -15x2

Combine like terms: 107x + -107x = 0
-14 + -107x + -15x2 = 0 + 15x2 + -15x2
-14 + -107x + -15x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
-14 + -107x + -15x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + 107x + 15x2) = 0

Factor a trinomial.
-1((7 + x)(2 + 15x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7

Subproblem 2

Set the factor '(2 + 15x)' equal to zero and attempt to solve: Simplifying 2 + 15x = 0 Solving 2 + 15x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 15x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 15x = 0 + -2 15x = 0 + -2 Combine like terms: 0 + -2 = -2 15x = -2 Divide each side by '15'. x = -0.1333333333 Simplifying x = -0.1333333333

Solution

x = {-7, -0.1333333333}

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