2(4x^2-49)=3(4x^2+28x+49)

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Solution for 2(4x^2-49)=3(4x^2+28x+49) equation: 


Simplifying
2(4x2 + -49) = 3(4x2 + 28x + 49)

Reorder the terms:
2(-49 + 4x2) = 3(4x2 + 28x + 49)
(-49 * 2 + 4x2 * 2) = 3(4x2 + 28x + 49)
(-98 + 8x2) = 3(4x2 + 28x + 49)

Reorder the terms:
-98 + 8x2 = 3(49 + 28x + 4x2)
-98 + 8x2 = (49 * 3 + 28x * 3 + 4x2 * 3)
-98 + 8x2 = (147 + 84x + 12x2)

Solving
-98 + 8x2 = 147 + 84x + 12x2

Solving for variable 'x'.

Reorder the terms:
-98 + -147 + -84x + 8x2 + -12x2 = 147 + 84x + 12x2 + -147 + -84x + -12x2

Combine like terms: -98 + -147 = -245
-245 + -84x + 8x2 + -12x2 = 147 + 84x + 12x2 + -147 + -84x + -12x2

Combine like terms: 8x2 + -12x2 = -4x2
-245 + -84x + -4x2 = 147 + 84x + 12x2 + -147 + -84x + -12x2

Reorder the terms:
-245 + -84x + -4x2 = 147 + -147 + 84x + -84x + 12x2 + -12x2

Combine like terms: 147 + -147 = 0
-245 + -84x + -4x2 = 0 + 84x + -84x + 12x2 + -12x2
-245 + -84x + -4x2 = 84x + -84x + 12x2 + -12x2

Combine like terms: 84x + -84x = 0
-245 + -84x + -4x2 = 0 + 12x2 + -12x2
-245 + -84x + -4x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-245 + -84x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(245 + 84x + 4x2) = 0

Factor a trinomial.
-1((35 + 2x)(7 + 2x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(35 + 2x)' equal to zero and attempt to solve:

Simplifying
35 + 2x = 0

Solving
35 + 2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-35' to each side of the equation.
35 + -35 + 2x = 0 + -35

Combine like terms: 35 + -35 = 0
0 + 2x = 0 + -35
2x = 0 + -35

Combine like terms: 0 + -35 = -35
2x = -35

Divide each side by '2'.
x = -17.5

Simplifying
x = -17.5

Subproblem 2
Set the factor '(7 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

Solving
7 + 2x = 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 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5
Solution
x = {-17.5, -3.5}

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